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Academic literature on the topic 'Homogeneous Operators'

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Published: 6 September 2023

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Journal articles on the topic "Homogeneous Operators"

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Burýšková, Věra, and Slavomír Burýšek. "On solvability of nonlinear operator equations and eigenvalues of homogeneous operators." Mathematica Bohemica 121, no. 3 (1996): 301–14. http://dx.doi.org/10.21136/mb.1996.125984.

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Sawano, Yoshihiro. "Maximal operator for pseudodifferential operators with homogeneous symbols." Michigan Mathematical Journal 59, no. 1 (April 2010): 119–42. http://dx.doi.org/10.1307/mmj/1272376028.

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Bekker, Borislava, and Miron B. Bekker. "On Selfadjoint Homogeneous Operators." Complex Analysis and Operator Theory 7, no. 1 (August 3, 2011): 9–31. http://dx.doi.org/10.1007/s11785-011-0175-9.

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Avsyankin, Oleg. "ON INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS IN MORREY SPACES." Eurasian Mathematical Journal 12, no. 1 (2021): 92–96. http://dx.doi.org/10.32523/2077-9879-2021-12-1-92-96.

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Grafakos, Loukas, and Rodolfo H. Torres. "Pseudodifferential operators with homogeneous symbols." Michigan Mathematical Journal 46, no. 2 (September 1999): 261–69. http://dx.doi.org/10.1307/mmj/1030132409.

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Korányi, Adam, and Gadadhar Misra. "New constructions of homogeneous operators." Comptes Rendus Mathematique 342, no. 12 (June 2006): 933–36. http://dx.doi.org/10.1016/j.crma.2006.04.002.

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Vasilescu, F. H. "Homogeneous operators and essential complexes." Glasgow Mathematical Journal 31, no. 1 (January 1989): 73–85. http://dx.doi.org/10.1017/s0017089500007576.

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The aim of this work is to present a new approach to the concept of essential Fredholm complex of Banach spaces ([10], [2]; see also [11], [4], [6], [7] etc. for further connections), by using non-linear homogeneous mappings. We obtain some generalized homotopic properties of the class of essential Fredholm complexes, in our sense, which are then applied to establish its relationship with similar concepts. We also prove the stability of this class under small perturbations with respect to the gap topology.
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Agbor, Dieudonne. "Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space." Journal of Mathematics Research 9, no. 6 (October 26, 2017): 67. http://dx.doi.org/10.5539/jmr.v9n6p67.

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We study some algebraic properties of Toeplitz operators with radial and quasi homogeneous symbols on the pluriharmonic Fock space over $\mathbb{C}^{n}$. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator, the zero-product problem for the product of two Toeplitz operators. Next we characterize the commutativity of Toeplitz operators with quasi homogeneous symbols and finally we study finite rank of the product of Toeplitz operators with quasi homogeneous symbols.
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de Oliveira, Souza, Jose J. S. de Figueiredo, and Lucas Freitas. "Redatuming Operators Analysis in Homogeneous Media." Acta Geophysica 63, no. 2 (April 2015): 414–31. http://dx.doi.org/10.2478/s11600-014-0248-z.

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Casadio Tarabusi, Enrico, and Alessandro Figà-Talamanca. "Drifted Laplace operators on homogeneous trees." Proceedings of the American Mathematical Society 135, no. 07 (July 1, 2007): 2165–76. http://dx.doi.org/10.1090/s0002-9939-07-08811-9.

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Dissertations / Theses on the topic "Homogeneous Operators"

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Stefanov, Atanas. "On homogeneous Calderón-Zygmund operators with rough kernels /." free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9951125.

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Connolly, Donal. "Pseudo-differential operators on homogeneous spaces." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/23926.

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In recent years, the use of Peter-Weyl theory (the theory of Fourier analysis on compact Lie groups) to define so-called 'global symbols' of operators on compact Lie groups has emerged as a fruitful technique to study pseudo-differential operators. The aim of this thesis is to discuss similar techniques in the setting of compact homogeneous spaces. The approach is to relate operators on homogeneous spaces to those on compact Lie groups, and then to utilize the recently developed techniques on such groups. Two methods of associating operators on homogeneous spaces with those on compact Lie groups, called projective and horizontal lifting, along with their properties, merits and problems are considered. A key tool used in this analysis is the notion of a difference operator. This thesis includes a detailed study of such operators and their properties, combined with comprehensive calculations involving such operators on the homogeneous spaces $\Sbb^{n-1} = \SO(n)/\SO(n-1)$. This thesis concludes with a generalization of the symbolic calculus on compact Lie groups developed by M. Ruzhansky and V. Turunen together with a collection of conjectures, which if proven would relate the generalization to pseudo-differential theory on homogeneous spaces.
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Allen, Robert Francis. "A class of operators with symbol on the bloch space of a bounded homogeneous domain." Fairfax, VA : George Mason University, 2009. http://hdl.handle.net/1920/4541.

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Thesis (Ph.D.)--George Mason University, 2009.
Vita: p. 158. Thesis director: Flavia Colonna. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics. Title from PDF t.p. (viewed Oct. 11, 2009). Includes bibliographical references (p. 150-157). Also issued in print.
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Sriskandasingam, Mayuran. "Non-homogeneous Boundary Value Problems of a Class of Fifth Order Korteweg-de Vries Equation posed on a Finite Interval." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1626357151760691.

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Alarcón, Daniel Núnez. "Sobre o teoremas de Bohnenblurt - Hille." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/8047.

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Os teoremas de Bohnenblust Hille, demonstrados em 1931 no prestigioso jornal Annals of Mathematics, foram utilizados como ferramentas muito úteis na solução do famoso Problema da convergência absoluta de Bohr. Após um longo tempo esquecidos, estes teoremas têm sido bastante explorados nos últimos anos. Este último quinquê- nio experimentou o surgimento de várias obras dedicadas a estimar as constantes de Bohnenblust Hille ([13, 18, 20, 26, 27, 39, 42, 44, 46, 53]) e também conexões inesperadas com a Teoria da Informação Quântica apareceram (ver, por exemplo, [38]). Há, de fato, quatro casos para serem investigados: polinomial (casos real e complexo) e multilinear (casos real e complexo). Podemos resumir em uma frase as principais informa ções dos trabalhos recentes: as constantes das desigualdades de Bohnenblust Hille são, em geral, extraordinariamente menores do que as primeiras estimativas tinham previsto. Neste trabalho apresentamos algumas das nossas pequenas contribuições ao estudo das constantes nas desigualdades de Bohnenblust-Hille, os quais encontram-se contidos em ([40, 41, 42, 44]).The Bohnenblust Hille theorems, proved in 1931 in the prestigious journal Annals of Mathematics, were used as very useful tools in the solution of the famous "Bohr's absolute convergence problem". After a long time overlooked, these theorems have been explored in the recent years. Last quinquennium experienced the rising of several works dedicated to estimate the Bohnenblust Hille constants ([13, 18, 20, 26, 27, 39, 42, 44, 46, 53]) and also unexpected connections with Quantum Information Theory appeared (see, e.g., [38]). There are in fact four cases to be investigated: polynomial (real and complex cases) and multilinear (real and complex cases). We can summarize in a sentence the main information from the recent preprints: the Bohnenblust Hille constants are, in general, extraordinarily smaller than the rst estimates predicted. In this work, we present some of our small contributions to the study of the constants of the inequalities Bohnenblust-Hille, these are contained in ([40, 41, 42, 44]).
Os teoremas de Bohnenblust Hille, demonstrados em 1931 no prestigioso jornal Annals of Mathematics, foram utilizados como ferramentas muito úteis na solução do famoso Problema da convergência absoluta de Bohr. Após um longo tempo esquecidos, estes teoremas têm sido bastante explorados nos últimos anos. Este último quinquê- nio experimentou o surgimento de várias obras dedicadas a estimar as constantes de Bohnenblust Hille ([13, 18, 20, 26, 27, 39, 42, 44, 46, 53]) e também conexões inesperadas com a Teoria da Informação Quântica apareceram (ver, por exemplo, [38]). Há, de fato, quatro casos para serem investigados: polinomial (casos real e complexo) e multilinear (casos real e complexo). Podemos resumir em uma frase as principais informa ções dos trabalhos recentes: as constantes das desigualdades de Bohnenblust Hille são, em geral, extraordinariamente menores do que as primeiras estimativas tinham previsto. Neste trabalho apresentamos algumas das nossas pequenas contribuições ao estudo das constantes nas desigualdades de Bohnenblust-Hille, os quais encontram-se contidos em ([40, 41, 42, 44])
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Wiesner, Dirk. "Polynomials in operator space theory /." Tönning ; Lübeck ; Marburg : Der Andere Verl, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=017610887&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Wiesner, Dirk. "Polynomials in operator space theory." Tönning Lübeck Marburg Der Andere Verl, 2008. http://d-nb.info/99429770X/04.

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Routin, Eddy. "Local Tb theorems and Hardy type inequalities." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00656023.

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In this thesis, we study local Tb theorems for singular integral operators in the setting of spaces of homogeneous type. We give a direct proof of the local Tb theorem with L^2 integrability on the pseudo- accretive system. Our argument relies on the Beylkin-Coifman-Rokhlin algorithm applied in adapted Haar wavelet basis and some stopping time results. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2, with an additional weak boundedness type hypothesis, which incorporates some Hardy type inequalities. We study the possibility of relaxing the support conditions on the pseudo-accretive system to a slight enlargement of the dyadic cubes. We also give a result in the case when, for practical reasons, hypotheses on the pseudo-accretive system are made on balls rather than dyadic cubes. Finally we study the particular case of perfect dyadic operators for which the proof gets much simpler. Our argument gives us the opportunity to study Hardy type inequalities. The latter are well known in the Euclidean setting, but seem to have been overlooked in spaces of homogeneous type. We prove that they hold without restriction in the dyadic setting. In the more general case of a ball B and its corona 2B\B, they can be obtained from some geometric conditions relative to the distribution of points in the homogeneous space. For example, we prove that some relative layer decay property suffices. We also prove that this property is implied by the monotone geodesic property of Tessera. Finally, we give some explicit examples and counterexamples in the complex plane to illustrate the relationship between the geometry of the homogeneous space and the validity of the Hardy type inequalities.
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9

McCormick, Kathryn. "Operator algebras, matrix bundles, and Riemann surfaces." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6469.

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Let $\overline{R}$ be a finitely bordered Riemann surface, and let $\mathfrak{E}_\rho(\overline{R})$ be a flat matrix $PU_n(\mathbb{C})$-bundle over $\overline{R}$. Let $\Gamma_c(\overline{R}, \mathfrak{E}(\overline{R}))$ denote the $C^*$-algebra of continuous cross-sections of $\mathfrak{E}(\overline{R})$, and let $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ denote the subalgebra consisting of the continuous holomorphic sections, i.e.~the continuous cross-sections that are holomorphic on the interior of $\overline{R}$. The algebra $\Gamma_c(\overline{R}, \mathfrak{E}(\overline{R}))$ is an example of an $n$-homogeneous $C^*$-algebra, and the subalgebra $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ is the principal object of study of this thesis. The algebras $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ appeared in the earlier works \cite{Abrahamse1976} and \cite{Blecher2000}. Operators that can be viewed as elements in $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ are the subject of \cite{Abrahamse1976}. The Morita theory of $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$, under the guise of a fixed-point algebra and in the special case of an annulus $R$, is studied in \cite[Ex.~8.3]{Blecher2000}. This thesis studies these algebras and their topological data $\mathfrak{E}_\rho(\overline{R})$ motivated by several problems in the theory of nonselfadjoint operator algebras. Boundary representations are an invariant of operator algebras that were introduced by Arveson in 1969. However, it took nearly 50 years to show that boundary representations existed in sufficient abundance in all cases. I show that every boundary representation of $\Gamma_c(\overline{R}, \mathfrak{E}(\overline{R}))$ for $\Gamma_h(\overline{R}, \mathfrak{E}(\overline{R}))$ is given by evaluation at some point $r \in \partial R$. As a corollary, the $C^*$-envelope of $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ is $\Gamma_c(\partial R, \mathfrak{E}(\partial R))$. Using the $C^*$-envelope, I show that for certain choices of fibre and base space, $\Gamma_h(\overline{R}, \mathfrak{E}_\rho(\overline{R}))$ is not completely isometrically isomorphic to $A(\overline{R})\otimes M_n(\mathbb{C})$ unless the representation $\rho$ is the trivial representation. I also show that $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ is an Azumaya over its center. Azumaya algebras are the ``pure-algebra'' analogues to $n$-homogeneous $C^*$-algebras \cite{Artin1969}. Thus the structure of the nonselfadjoint subalgebra $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ reflects some of the structure of its $C^*$-envelope (which is $n$-homogeneous). Finally, I answer a question raised in \cite[Ex.~8.3]{Blecher2000} on the $cb$ and strong Morita theory of $\Gamma_h(\overline{R},\mathfrak{E}_\rho(\overline{R}))$, showing in particular that $\Gamma_h(\overline{R},\mathfrak{E}_\rho(\overline{R}))$ is $cb$ Morita equivalent to its center $A(\overline{R})$. As suggested in \cite[Ex.~8.3]{Blecher2000}, I provide additional evidence that $\Gamma_h(\overline{R},\mathfrak{E}_\rho(\overline{R}))$ may not be strongly Morita equivalent to its center. This evidence, in turn, suggests that there may be a Brauer group -like analysis for these algebras.
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Arias, Marco Teresa. "Study of homogeneous DÀtri spaces, of the Jacobi operator on g.o. spaces and the locally homogeneous connections on 2-dimensional manifolds with the help of Mathematica." Doctoral thesis, Universitat de València, 2007. http://hdl.handle.net/10803/9954.

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Nowadays, the concept of homogeneity is one of the fundamental notions in geometry although its meaning must be always specified for the concrete situations. In this thesis, we consider the homogeneity of Riemannian manifolds and the homogeneity of manifolds equipped with affine connections. The first kind of homogeneity means that, for every smooth Riemannian manifold (M, g), its group of isometries I(M) is acting transitively on M. Part I of this thesis fits into this philosophy. Afterwards in Part II, we treat the homogeneity concept of affine connections. This homogeneity means that, for every two points of a manifold, there is an affine diffeomorphism which sends one point into another. In particular, we consider a local version of the homogeneity, that is, we accept that the affine diffeomorphisms are given only locally, i.e., from a neighborhood onto a neighborhood. More specifically, we devote the first Chapter of Part I to make a brief overview of some special kinds of homogeneous Riemannian manifolds which will be of special relevance in Part I and to show how the software MATHEMATICA© becomes useful. For that, we prove that "the three-parameter families of flag manifolds constructed by N. R. Wallach in "Compact homogeneous Riemannian manifols with strictly positive curvature, Ann. of Math. 96 (1972), p. 276-293" are D'Atri spaces if and only if they are naturally reductive spaces. Thus, we improve the previous results given by D'Atri, Nickerson and by Arias-Marco, Naveira.Moreover, in Chapter 2 we obtain the complete 4-dimensional classification of homogeneous spaces of type A. This allows us to prove correctly that every 4-dimensional homogeneous D'Atri space is naturally reductive. Therefore, we correct, complete and improve the results presented by Podestà, Spiro, Bueken and Vanhecke. Chapter 3 is devoted to prove that the curvature operator has constant osculating rank over g.o. spaces. It is mean that a real number 'r' exists such that under some assumptions, the higher order derivatives of the curvature operator from 1 to r are linear independent and from 1 to r + 1 are linear dependent. As a consequence, we also present a method valid on every g.o. space to solve the Jacobi equation. This method extends the method given by Naveira and Tarrío for naturally reductive spaces. In particular, we prove that the Jacobi operator on Kaplan's example (the first known g.o. space that it is not naturally reductive) has constant osculating rank 4. Moreover, we solve the Jacobi equation along a geodesic on Kaplan's example using the new method and the well-known method used by Chavel, Ziller and Berndt,Tricerri, Vanhecke. Therefore, we are able to present the main differences between both methods.In Part II, we classify (locally) all locally homogeneous affine connections with arbitrary torsion on two-dimensional manifolds. Therefore, we generalize the result given by Opozda for torsion-less case. Moreover, from our computations we obtain interesting consequences as the relation between the classifications given for the torsion less-case by Kowalski, Opozda and Vlá ek. In addition, we obtain interesting consequences about flat connections with torsion.In general, the study of these problems sometimes requires a big number of straightforward symbolic computations. In such cases, it is a quite difficult task and a lot of time consuming, try to make correctly this kind of computations by hand. Thus, we try to organize our computations in (possibly) most systematic way so that the whole procedure is not excessively long. Also, because these topics are an ideal subject for a computer-aided research, we are using the software MATHEMATICA©, throughout this work. But we put stress on the full transparency of this procedure.
En esta tesis, se consideran dos tipos bien diferenciados de homogeneidad: la de las variedades riemannianas y la de las variedades afines. El primer tipo de homogeneidad se define como aquel que tiene la propiedad de que el grupo de isometrías actúa transitivamente sobre la variedad. La Parte I, recoge todos los resultados que hemos obtenido en esta dirección. Sin embargo, en la Parte II se presentan los resultados obtenidos sobre conexiones afines homogéneas. Una conexión afín se dice homogénea si para cada par de puntos de la variedad existe un difeomorfismo afín que envía un punto en otro. En este caso, se considera una versión local de homogeneidad. Más específicamente, la Parte I de esta tesis está dedicada a probar que "las familias 3-paramétricas de variedades bandera construidas por Wallach son espacios de D'Atri si y sólo si son espacios naturalmente reductivos". Más aún, en el segundo Capítulo, se obtiene la clasificación completa de los espacios homogéneos de tipo A cuatro dimensionales que permite probar correctamente que todo espacio de D'Atri homogéneo de dimensión cuatro es naturalmente reductivo.Finalmente, en el tercer Capítulo se prueba que en cualquier g.o. espacio el operador curvatura tiene rango osculador constante y, como consecuencia, se presenta un método para resolver la ecuación de Jacobi sobre cualquier g.o. espacio. La Parte II se destina a clasificar (localmente) todas las conexiones afines localmente homogéneas con torsión arbitraria sobre variedades 2-dimensionales. Para finalizar el cuarto Capítulo, se prueban algunos resultados interesantes sobre conexiones llanas con torsión.En general, el estudio de estos problemas requiere a veces, un gran número de cálculos simbólicos aunque sencillos. En dichas ocasiones, realizarlos correctamente a mano es una tarea ardua que requiere mucho tiempo. Por ello, se intenta organizar todos estos cálculos de la manera más sistemática posible de forma que el procedimiento no resulte excesivamente largo. Este tipo de investigación es ideal para utilizar la ayuda del ordenador; así, cuando resulta conveniente, utilizamos la ayuda del software MATHEMATICA para desarrollar con total transparencia el método de resolución que más se adecua a cada uno de los problemas a resolver.
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Books on the topic "Homogeneous Operators"

1

Smooth homogeneous structures in operator theory. Boca Raton: Chapman & Hall/CRC, 2005.

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Mass.) AMS Special Session on Radon Transforms and Geometric Analysis (2012 Boston. Geometric analysis and integral geometry: AMS special session in honor of Sigurdur Helgason's 85th birthday, radon transforms and geometric analysis, January 4-7, 2012, Boston, MA ; Tufts University Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces, January 8-9, 2012, Medford, MA. Edited by Quinto, Eric Todd, 1951- editor of compilation, Gonzalez, Fulton, 1956- editor of compilation, Christensen, Jens Gerlach, 1975- editor of compilation, and Tufts University. Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces. Providence, Rhode Island: American Mathematical Society, 2013.

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Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory. Heidelberg: Birkhäuser, 2014.

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Epstein, Charles L., and Rafe Mazzeo. The Model Solution Operators. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0004.

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This chapter introduces the model problems and the solution operator for the associated heat equations. These operators give a good approximation for the behavior of the heat kernel in neighborhoods of different types of boundary points. The chapter states and proves the elementary features of these operators and shows that the model heat operators have an analytic continuation to the right half plane. It first considers the model problem in 1-dimension and in higher dimensions before discussing the solution to the homogeneous Cauchy problem. It then describes the first steps toward perturbation theory and constructs the solution operator for generalized Kimura diffusions on a suitable scale of Hölder spaces. It also defines the resolvent families and explains why the estimates obtained here are not adequate for the perturbation theoretic arguments needed to construct the solution operator for generalized Kimura diffusions.
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Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
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Beltita, Daniel. Smooth Homogeneous Structures in Operator Theory. Taylor & Francis Group, 2005.

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Beltita, Daniel. Smooth Homogeneous Structures in Operator Theory. Taylor & Francis Group, 2019.

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Beltita, Daniel. Smooth Homogeneous Structures in Operator Theory. Taylor & Francis Group, 2005.

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Epstein, Charles L., and Rafe Mazzeo. The Resolvent Operator. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0011.

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This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.
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Tolsa, Xavier. Analytic Capacity, the Cauchy Transform, and Non-Homogeneous Calderón-Zygmund Theory. Springer International Publishing AG, 2016.

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Book chapters on the topic "Homogeneous Operators"

1

Korányi, Adam. "Differential Operators." In Analysis and Geometry on Complex Homogeneous Domains, 243–55. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1366-6_18.

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Wong, M. W. "Group Actions and Homogeneous Spaces." In Wavelet Transforms and Localization Operators, 141–42. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8217-0_24.

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Ruzhansky, Michael, and Ville Turunen. "Pseudo-differential Operators on Homogeneous Spaces." In Pseudo-Differential Operators and Symmetries, 667–81. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-8514-9_18.

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Ortner, Norbert, and Peter Wagner. "Fundamental Matrices of Homogeneous Systems." In Fundamental Solutions of Linear Partial Differential Operators, 333–69. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20140-5_5.

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Biroli, Marco, and Umberto Mosco. "Sobolev Inequalities on Homogeneous Spaces." In Potential Theory and Degenerate Partial Differential Operators, 311–24. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0085-4_1.

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Helgason, Sigurdur. "Solvability of Invariant Differential Operators on Homogeneous Manifolds." In Differential Operators on Manifolds, 281–311. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11114-3_5.

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Rabinovich, Vladimir S., and Steffen Roch. "Integral Operators with Shifts on Homogeneous Groups." In Factorization, Singular Operators and Related Problems, 255–71. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0227-0_17.

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Bott, Raoul. "The Index Theorem for Homogeneous Differential Operators." In Raoul Bott Collected Papers, 163–83. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-5367-9_5.

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Yamazaki, Masao. "Propagation of quasi-homogeneous microlocal singularities of solutions to nonlinear partial differential equations." In Pseudo-Differential Operators, 442–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077755.

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Drábek, Pavel. "On the Fredholm Alternative for Nonlinear Homogeneous Operators." In Applied Nonlinear Analysis, 41–48. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/0-306-47096-9_4.

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Conference papers on the topic "Homogeneous Operators"

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Hou, Yuexia. "Global Lorentz estimates for hypoelliptic operators with drift on homogeneous group." In International Conference on Electronic Information Engineering and Computer Technology (EIECT 2021), edited by Fengjie Cen, Sahil Verma, and N. Rajathi. SPIE, 2021. http://dx.doi.org/10.1117/12.2624848.

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Lancellotti, V., B. P. de Hon, and A. G. Tijhuis. "Linear embedding via Green's operators for 3-D scattering from piecewise homogeneous bodies." In 2010 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2010. http://dx.doi.org/10.1109/iceaa.2010.5651114.

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Mironchenko, Andrii, Navid Noroozi, Christoph Kawan, and Majid Zamani. "A small-gain approach to ISS of infinite networks with homogeneous gain operators." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683337.

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Kurdila, A., and J. Li. "Relaxation Methods for Nonlinear Dynamics and Hysteresis Operators." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8062.

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Abstract Previous research has demonstrated that rigorous modeling and identification theory can be derived for structural dynamical models that incorporate control influence operators that are static Krasnoselskii-Pokrovskii integral hysteresis operators. Experimental evidence likewise has shown that some dynamic hysteresis models provide more accurate representations of a class of structural systems actuated by some active materials including shape memory alloys and piezoceramics. In this paper, we show that the representation of control influence operators via static hysteresis operators can be interpreted in terms of a homogeneous Young’s measure. Within this framework, we subsequently derive dynamic hysteresis operators represented in terms of Young’s measures that are parameterized in time. We show that the resulting integrodifferential equations are similar to the class of relaxed controls discussed by Warga [10], Garnkrelidze [24], and Roubicek [25]. The formulation presented here differs from that studied in [10], [24] and [25] in that the kernel of the hysteresis operator is a history dependent functional, as opposed to Caratheodory integral satisfying a growth condition. The theory presented provides representations of dynamic hysteresis operators that have provided good agreement with experimental behavior in some active materials.
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Elena, Miroshnikova. "Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904637.

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Zhang, Junjian, Guoyi Ke, and Z. Charlie Zheng. "Time-Domain Simulation of Ultrasound Propagation With Fractional Laplacian." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65966.

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The simulation is developed for the purpose of simulating ultrasound propagation through biological tissues. The simulation is based on the time-domain conservation laws with the governing equations for acoustic pressure and velocity, with frequency dependent absorption and dispersion effects. We use forward differencing for velocity and backward differencing for pressure on the non-fractional derivative operator terms in spatial discretization. The fractional Laplacian operators are treated as Riesz derivatives. The shifted standard Grunwald approximation method is used to solve fractional derivative operator terms. To accommodate complicated biological tissue geometries, an immersed boundary method is developed that enables a Cartesian computational grid mesh to be used. The results are compared with those for a non-absorption homogeneous medium to discuss absorption and dispersion effects of biological material.
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Andrade, Matheus Guedes de, Franklin De Lima Marquezino, and Daniel Ratton Figueiredo. "Characterizing the Relationship Between Unitary Quantum Walks and Non-Homogeneous Random Walks." In Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ctd.2021.15756.

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Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the relationship between quantum and random walks has been recently discussed in specific scenarios, this work establishes a formal equivalence between the two processes on arbitrary finite graphs and general conditions for shift and coin operators. It requires empowering random walks with time heterogeneity, where the transition probability of the walker is non-uniform and time dependent. The equivalence is obtained by equating the probability of measuring the quantum walk on a given node of the graph and the probability that the random walk is at that same node, for all nodes and time steps. The first result establishes procedure for a stochastic matrix sequence to induce a random walk that yields the exact same vertex probability distribution sequence of any given quantum walk, including the scenario with multiple interfering walkers. The second result establishes a similar procedure in the opposite direction. Given any random walk, a time-dependent quantum walk with the exact same vertex probability distribution is constructed. Interestingly, the matrices constructed by the first procedure allows for a different simulation approach for quantum walks where node samples respect neighbor locality and convergence is guaranteed by the law of large numbers, enabling efficient (polynomial-time) sampling of quantum graph trajectories. Furthermore, the complexity of constructing this sequence of matrices is discussed in the general case.
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Hadjisotiriou, George, Kiarash Mansour Pour, and Denis Voskov. "Application of Deep Neural Networks to the Operator Space of Nonlinear PDE for Physics-Based Proxy Modelling." In SPE Reservoir Simulation Conference. SPE, 2023. http://dx.doi.org/10.2118/212217-ms.

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Abstract In this study, we utilize deep neural networks to approximate operators of a nonlinear partial differential equation (PDE), within the Operator-Based Linearization (OBL) simulation framework, and discover the physical space for a physics-based proxy model with reduced degrees of freedom. In our methodology, observations from a high-fidelity model are utilized within a supervised learning scheme to directly train the PDE operators and improve the predictive accuracy of a proxy model. The governing operators of a pseudo-binary gas vaporization problem are trained with a transfer learning scheme. In this two-stage methodology, labeled data from an analytical physics-based approximation of the operator space are used to train the network at the first stage. In the second stage, a Lebesgue integration of the shocks in space and time is used in the loss function by the inclusion of a fully implicit PDE solver directly in the neural network's loss function. The Lebesgue integral is used as a regularization function and allows the neural network to discover the operator space for which the difference in shock estimation is minimal. Our Physics-Informed Machine Learning (PIML) methodology is demonstrated for an isothermal, compressible, two-phase multicomponent gas-injection problem. Traditionally, neural networks are used to discover hidden parameters within the nonlinear operator of a PDE. In our approach, the neural network is trained to match the shocks of the full-compositional model in a 1D homogeneous model. This training allows us to significantly improve the prediction of the reduced-order proxy model for multi-dimensional highly heterogeneous reservoirs. With a relatively small amount of training, the neural network can learn the operator space and decrease the error of the phase-state classification of the compositional transport problem. Furthermore, the accuracy of the breakthrough time prediction is increased therefore improving the usability of the proxy model for more complex cases with more nonlinear physics.
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Perre, Patrick, and Ian Turner. "A physical interpretation of the use of fractional operators for modelling the drying process." In 21st International Drying Symposium. Valencia: Universitat Politècnica València, 2018. http://dx.doi.org/10.4995/ids2018.2018.7885.

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Fractional order derivatives provide useful alternatives to their integer order counterparts due to their ability to model memory and other properties of the porous medium, such as nonlocal behaviour. These phenomena are driven by the constrained interactions within the complex and non-homogeneous microstructures evident at the pore scale. In this work, we investigate the suitability of time and space fractional operators for modelling drying processes and provide a physical interpretation of these operators. At first, the concept and the general formulation in the case of a 1-D finite domain is summarised. Then a selection of simulations allowed us to analyse the physical effects of these operators on the solution. In particular, we elucidate:(I )the ability of these operators to break the fundamental relationship between mean square displacement and time in the simple example of diffusion in an open space, (ii) the caution to be taken with the formulation of boundary conditions and source terms to obtain consistent balance equations, (iii) the effect of fractional in space diffusion as a way to alter the MC profiles compared to standard diffusion, therefore potentially avoiding the dependence of the diffusivity on the variable Keywords: Fractional Calculus; Transport in Porous Media; Finite Volume Method; Matrix Transfer Technique; Matrix Functions.
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Graber, H. L., J. Chang, R. L. Barbour, and R. Aronson. "Evaluation of Spatial Variations in the Time and Frequency Dependence of Imaging Operators for Diffusion Tomography." In Advances in Optical Imaging and Photon Migration. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/aoipm.1994.apmpdwi.99.

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Employing the framework of a perturbation model for optical diffusion tomography, the sensitivity and selectivity attainable from optical time- and frequency-domain, including phased array, measurements, are compared and contrasted. Monte Carlo simulations were used to calculate impulse-response functions in the interior of several homogeneous media. From the results, the impact on detected light due to small localized changes in absorption cross-section were computed. A feature unique to the frequency domain is the ability to qualitatively modify the depth profile of the weight amplitude by employing several sources in a phased array. In the case of single-source transmission measurements, a time-resolved measurement with a short integration time leads to enhanced ability to resolve deep-lying structures, by increasing the weight in deep regions relative to those near the surface. In contrast, as the source modulation frequency is increased in a frequency-domain measurement, the weight amplitude drops off most rapidly in regions farthest from the boundaries, and more slowly in more superficial regions. The significance of these findings for perturbation-based image recovery schemes is discussed.
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Reports on the topic "Homogeneous Operators"

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Esparza and Westine. L51482 Well Casing Response to Buried Explosive Detonations. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), July 1985. http://dx.doi.org/10.55274/r0010272.

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Occasionally, buried explosives are used within proximity of producing oil and gas wells which increases the stresses in the casing near the explosion which may result in failure of the well. A procedure was needed for predicting the maximum stresses in producing oil and gas wells, specifically the well casing, induced by nearby, buried, explosive detonations. An extensive experimental and analytical program were funded and performed over a six (6) year period 1975-1981. The program was divided into two (2) parts: In the first part, similitude theory, empirical analyses and test data were used to derive equations for estimating maximum ground displacement and particle velocity. The ground motions provided the forcing function imparted to a buried pipeline. In the second part, similitude theory, conservation of mass and momentum, and approximate energy methods were used to derive functional relationships for the maximum pipe strains and stresses. Experimental data from more than sixty (60) field tests ere used to develop equations for estimating maximum pipe stresses induced by point and parallel line explosive sources buried in homogeneous soil media. The pipe stress and ground motion data from these experiments were used to develop an equation for computing an effective standoff distance so that the point source soil equations could be used to approximate the casing response. The large amount of data used and the wide range of these data make the solutions applicable to most blasting situations near producing oil and gas wells. This report provides comprehensive and detailed information for pipeline as well as oil and gas operators to predict the effect of buried explosives and thus the safety of a well(s) while in-service through proper assessment of stresses and guidelines for the appropriate selection of explosive charges, techniques and methods. This will avoid unexpected damages, operational costs, provide guidance for \operator qualification\" for blasting near in-service wells and minimize liabilities to the operator.
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Deschamps, Robert, and Henschel. PR-420-133721-R01 Comparison of Radar Satellite Methods for Observation of Stability. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), July 2015. http://dx.doi.org/10.55274/r0010840.

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This report discusses the use of Synthetic Aperture Radar (SAR) satellites for monitoring above ground pipelines and buried pipeline Rights-Of-Way (ROWs) using Interferometric Synthetic Aperture Radar (InSAR) techniques. The main thrust of the research was to evaluate the suitability of above-ground pipeline support members as InSAR measurement points, and to adapt existing techniques to allow for precise monitoring of jacking and subsidence caused by permafrost degradation and dynamics. The study site at Prudhoe Bay, Alaska includes more than 60,000 horizontal pipeline supports. The known locations of supports were used to identify and isolate supports in the radar imagery, and the phase and intensity of supports were analyzed to determine their ability to provide reliable estimates of deformation. An additional component of this research was the comparison of two satellites operating at different frequencies, RADARSAT-2 operating at C-band and TerraSAR-X operating at X-band. One year of data was acquired with both sensors in similar acquisition geometries and resolutions, at 24-day intervals for RADARSAT-2 and 11-day intervals for TerraSAR-X. Recommendations are made on the choice of wavelength and concerning future work in this area. A list of technical requirements is also provided. The technologies for obtaining ground deformation estimates from natural targets, coherent targets and homogeneous and distributed targets are explained and supported by three operational case-studies in different environments. The work should provide above-ground pipeline operators working in permafrost areas with a clear view of the current state of research towards the operationalization of InSAR monitoring, but also of current operational capabilities in other pipeline applications, including ROW geohazard monitoring and monitoring of buried pipelines crossing Enhanced Oil Recovery (EOR) fields.
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