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Journal articles on the topic 'Homogeneous Operators'

Author: Grafiati

Published: 6 September 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Borho, W., and J. L. Brylinski. "Differential operators on homogeneous spaces. III." Inventiones Mathematicae 80, no. 1 (February 1985): 1–68. http://dx.doi.org/10.1007/bf01388547.

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12

Shyam Roy, Subrata. "Homogeneous Operators, Jet Construction and Similarity." Complex Analysis and Operator Theory 5, no. 1 (July 22, 2009): 261–81. http://dx.doi.org/10.1007/s11785-009-0024-2.

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13

Luo, Xuebo. "Liouville's theorem for homogeneous differential operators." Communications in Partial Differential Equations 22, no. 11-12 (January 1997): 1837–48. http://dx.doi.org/10.1080/03605309708821322.

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14

Ioku, Norisuke, Giorgio Metafune, Motohiro Sobajima, and Chiara Spina. "Lp–Lq estimates for homogeneous operators." Communications in Contemporary Mathematics 18, no. 03 (March 22, 2016): 1550037. http://dx.doi.org/10.1142/s0219199715500376.

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15

Bruneau, Laurent, Jan Dereziński, and Vladimir Georgescu. "Homogeneous Schrödinger Operators on Half-Line." Annales Henri Poincaré 12, no. 3 (February 5, 2011): 547–90. http://dx.doi.org/10.1007/s00023-011-0078-3.

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16

Dell’Atti, Marta, and Pierandrea Vergallo. "Classification of degenerate non-homogeneous Hamiltonian operators." Journal of Mathematical Physics 64, no. 3 (March 1, 2023): 033505. http://dx.doi.org/10.1063/5.0135134.

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We investigate non-homogeneous Hamiltonian operators composed of a first order Dubrovin–Novikov operator and an ultralocal one. The study of such operators turns out to be fundamental for the inverted system of equations associated with a class of Hamiltonian scalar equations. Often, the involved operators are degenerate in the first order term. For this reason, a complete classification of the operators with a degenerate leading coefficient in systems with two and three components is presented.

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17

Kaiser, Cornelia. "Calderón-Zygmund operators with operator-valued kernel on homogeneous Besov spaces." Mathematische Nachrichten 282, no. 1 (December 19, 2008): 69–85. http://dx.doi.org/10.1002/mana.200610722.

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18

Vergallo, Pierandrea, and Raffaele Vitolo. "Projective geometry of homogeneous second-order Hamiltonian operators." Nonlinearity 36, no. 10 (September 1, 2023): 5311–33. http://dx.doi.org/10.1088/1361-6544/acf269.

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Abstract We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such operators in dimension n and 3-forms in dimension n + 1. In this way we classify second-order Hamiltonian operators using the known classification of 3-forms in dimensions ⩽ 9 . As a by-product, we identify such operators as linear line congruences, that are distinguished algebraic varieties in Plücker’s space of lines. Systems of first-order conservation laws that are Hamiltonian with respect to such operators are also explicitly found. The geometry and integrability of the systems is discussed in detail.

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19

Vignatti, Maria Amelia, Oscar Salinas, and Silvia Hartzstein. "Two-weighted inequalities for maximal operators related to Schrödinger differential operator." Forum Mathematicum 32, no. 6 (November 1, 2020): 1415–39. http://dx.doi.org/10.1515/forum-2019-0243.

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AbstractWe introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that connect maximal operators naturally associated to Schrödinger operators.

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20

Bordin, Benjamin, and Dicesar Lass Fernandes. "Singular Integral Operators with Operator-Valued Kernels on Spaces of Homogeneous Type." Zeitschrift für Analysis und ihre Anwendungen 11, no. 2 (1992): 154–66. http://dx.doi.org/10.4171/zaa/617.

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21

Kumar, Vishvesh. "Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups." Forum Mathematicum 31, no. 2 (March 1, 2019): 275–82. http://dx.doi.org/10.1515/forum-2018-0155.

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AbstractLet G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space {G/H}. We present a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert–Schmidt operators. We also give a characterization of and a trace formula for the trace class pseudo-differential operators on the homogeneous space {G/H}.

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22

Ben Said, Mona. "Kramers–Fokker–Planck operators with homogeneous potentials." Mathematical Methods in the Applied Sciences 45, no. 2 (September 29, 2021): 914–27. http://dx.doi.org/10.1002/mma.7822.

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23

Avsyankin, O. G. "Multidimensional integral operators with homogeneous-difference kernels." Differential Equations 48, no. 1 (January 2012): 65–71. http://dx.doi.org/10.1134/s001226611110077.

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24

Pradolini, Gladis, and Oscar Salinas. "Maximal operators on spaces of homogeneous type." Proceedings of the American Mathematical Society 132, no. 2 (June 30, 2003): 435–41. http://dx.doi.org/10.1090/s0002-9939-03-07079-5.

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25

Kogoj, Alessia Elisabetta, and Ermanno Lanconelli. "Link of groups and homogeneous Hörmander operators." Proceedings of the American Mathematical Society 135, no. 07 (July 1, 2007): 2019–31. http://dx.doi.org/10.1090/s0002-9939-07-08646-7.

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26

Gorbounov, Vassily, Fyodor Malikov, and Vadim Schechtman. "On chiral differential operators over homogeneous spaces." International Journal of Mathematics and Mathematical Sciences 26, no. 2 (2001): 83–106. http://dx.doi.org/10.1155/s0161171201020051.

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We give a classification and construction of chiral algebras of differential operators over semisimple algebraic groupsGand over homogeneous spacesG/NandG/PwhereNis a nilpotent andPa parabolic subgroup.

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27

Arazy, Jonathan, and Genkai Zhang. "Homogeneous multiplication operators on bounded symmetric domains." Journal of Functional Analysis 202, no. 1 (August 2003): 44–66. http://dx.doi.org/10.1016/s0022-1236(02)00072-1.

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28

Vaksman, L. L. "Integral intertwining operators and quantum homogeneous spaces." Theoretical and Mathematical Physics 105, no. 3 (December 1995): 1476–83. http://dx.doi.org/10.1007/bf02070867.

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29

WILKINS, DAVID R. "HOMOGENEOUS VECTOR BUNDLES AND COWEN-DOUGLAS OPERATORS." International Journal of Mathematics 04, no. 03 (June 1993): 503–20. http://dx.doi.org/10.1142/s0129167x93000261.

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In this paper we obtain an algebraic classification of all homogeneous Hermitian holomorphic vector bundles of arbitrary rank over a bounded symmetric domain. This classification result is used in order to classify, up to unitary equivalence, all irreducible homogeneous bounded linear operators on a separable infinite-dimensional Hilbert space that belong to the Cowen-Douglas class B2 (∆), where ∆ is the open unit disk.

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30

Camus, Brice. "Fundamental solutions of homogeneous elliptic differential operators." Bulletin des Sciences Mathématiques 130, no. 3 (April 2006): 264–68. http://dx.doi.org/10.1016/j.bulsci.2005.12.001.

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31

Martin, Mircea, and Pawel Szeptycki. "Convolution operators with homogeneous kernels and applications." Indiana University Mathematics Journal 46, no. 3 (1997): 0. http://dx.doi.org/10.1512/iumj.1997.46.1405.

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32

Kolesnikov, P. S. "Homogeneous Averaging Operators on Semisimple Lie Algebras." Algebra and Logic 53, no. 6 (January 2015): 510–11. http://dx.doi.org/10.1007/s10469-015-9313-1.

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33

Pankov, A. A. "Homogeneous random pseudodifferential operators of first order." Ukrainian Mathematical Journal 37, no. 6 (1986): 602–5. http://dx.doi.org/10.1007/bf01057428.

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34

Mirotin, Adolf R. "Hausdorff operators on homogeneous spaces of locally compact groups." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 30, 2020): 28–35. http://dx.doi.org/10.33581/2520-6508-2020-2-28-35.

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Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.

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35

Antonevich, A. B. "Right-Sided Invertibility of Binomial Functional Operators and Graded Dichotomy." Contemporary Mathematics. Fundamental Directions 67, no. 2 (December 15, 2021): 208–36. http://dx.doi.org/10.22363/2413-3639-2021-67-2-208-236.

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In this paper, we consider the right-sided invertibility problem for binomial functional operators. It is known that such operators are invertible iff there exists dichotomy of solutions of the homogeneous equation. New property of solutions of the homogeneous equation named graded dichotomy is introduced and it is proved that right-sided invertibility of binomial functional operators is equivalent to existence of graded dichotomy.

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36

Ruzhansky, Michael, Durvudkhan Suragan, and Nurgissa Yessirkegenov. "Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces." Fractional Calculus and Applied Analysis 21, no. 3 (June 26, 2018): 577–612. http://dx.doi.org/10.1515/fca-2018-0032.

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AbstractWe analyze local (central) Morrey spaces, generalized local (central) Morrey spaces and Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood maximal operator, Bessel-Riesz operators, generalized Bessel-Riesz operators and generalized fractional integral operators in generalized local (central) Morrey spaces on homogeneous groups is shown. Moreover, we prove the boundedness of the modified version of the generalized fractional integral operator and Olsen type inequalities in Campanato spaces and generalized local (central) Morrey spaces on homogeneous groups, respectively. Our results extend results known in the isotropic Euclidean settings, however, some of them are new already in the standard Euclidean cases.

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37

Polyakov, Andrey. "Homogeneous Lyapunov functions for homogeneous infinite dimensional systems with unbounded nonlinear operators." Systems & Control Letters 148 (February 2021): 104854. http://dx.doi.org/10.1016/j.sysconle.2020.104854.

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38

Saranchuk, Yu, and A. Shishkin. "General elementary solution of a 𝑞-sided convolution type homogeneous equation." St. Petersburg Mathematical Journal 34, no. 4 (July 26, 2023): 695–713. http://dx.doi.org/10.1090/spmj/1774.

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Exponential polynomials satisfying a homogeneous equation of convolution type are called its elementary solutions. The article is devoted to convolution-type operators in the complex domain that generalize the well-known operators of q q -sided convolution and π \pi -convolution. The properties of such operators are investigated and the general form of elementary solutions (general elementary solution) of a homogeneous equation of q q -sided convolution type is described.

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39

Haji-Badali, Ali, and Amirhesam Zaeim. "Commutative curvature operators over four-dimensional homogeneous manifolds." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550123. http://dx.doi.org/10.1142/s0219887815501236.

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Four-dimensional pseudo-Riemannian homogeneous spaces whose isotropy is non-trivial with commuting curvature operators have been studied. The only example of homogeneous Einstein four-manifold which is curvature-Ricci commuting but not semi-symmetric has been presented. Non-trivial examples of semi-symmetric homogeneous four-manifolds which are not locally symmetric, also Jacobi–Jacobi commuting manifolds which are not flat have been presented.

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40

Hu, Guoen, Haibo Lin, and Dachun Yang. "Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type." Abstract and Applied Analysis 2008 (2008): 1–21. http://dx.doi.org/10.1155/2008/237937.

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WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

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41

Gunawan, Hendra, Denny Ivanal Hakim, Yoshihiro Sawano, and Idha Sihwaningrum. "Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/809704.

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We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

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42

Hu, Guoen, Shanzhen Lu, and Dachun Yang. "Boundedness of rough singular integral operators on homogeneous Herz spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 2 (April 1999): 201–23. http://dx.doi.org/10.1017/s1446788700039318.

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AbstractThe authors establish the boundedness on the Herz spaces and the weak Herz spaces for a large class of rough singular integral operators and their corresponding fractional versions. Applications are given to Fefferman's rough singular integral operators, their fractional versions, their commutators with BMO() functions and Ricci-Stein oscillatory singular integral operators. Some new results are obtained.

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43

Ding, Yong, and Shanzhen Lu. "Hardy spaces estimates for multilinear operators with homogeneous kernels." Nagoya Mathematical Journal 170 (2003): 117–33. http://dx.doi.org/10.1017/s0027763000008552.

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AbstractIn this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.

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44

Slimane, A. "Spaces generated by the cone of sublinear operators." Carpathian Mathematical Publications 10, no. 2 (December 31, 2018): 376–86. http://dx.doi.org/10.15330/cmp.10.2.376-386.

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This paper deals with a study on classes of non linear operators. Let $SL(X,Y)$ be the set of all sublinear operators between two Riesz spaces $X$ and $Y$. It is a convex cone of the space $H(X,Y)$ of all positively homogeneous operators. In this paper we study some spaces generated by this cone, therefore we study several properties, which are well known in the theory of Riesz spaces, like order continuity, order boundedness etc. Finally, we try to generalise the concept of adjoint operator. First, by using the analytic form of Hahn-Banach theorem, we adapt the notion of adjoint operator to the category of positively homogeneous operators. Then we apply it to the class of operators generated by the sublinear operators.

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45

Al-Qassem, Hussain, and Ahmad Al-Salman. "Rough Marcinkiewicz integral operators." International Journal of Mathematics and Mathematical Sciences 27, no. 8 (2001): 495–503. http://dx.doi.org/10.1155/s0161171201006548.

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We study the Marcinkiewicz integral operatorM𝒫f(x)=(∫−∞∞|∫|y|≤2tf(x−𝒫(y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where𝒫is a polynomial mapping fromℝnintoℝdandΩis a homogeneous function of degree zero onℝnwith mean value zero over the unit sphereSn−1. We prove anLpboundedness result ofM𝒫for roughΩ.

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46

Morales-Ramos, Miguel Antonio, Raul Quiroga-Barranco, and Armando Sanchez-Nungaray. "Toeplitz Operators, Pseudo-Homogeneous Symbols, and Moment Maps on the Complex Projective Space." Journal of Function Spaces 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/1730920.

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Following previous works for the unit ball due to Nikolai Vasilevski, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in terms of moment maps is developed. This leads us to the introduction of a new family of symbols, extended pseudo-homogeneous, that provide larger commutative Banach algebras generated by Toeplitz operators. This family of symbols provides new commutative Banach algebras generated by Toeplitz operators on the unit ball.

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47

Meda, Stefano. "On non-isotropic homogeneous Lipschitz spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 2 (October 1989): 240–55. http://dx.doi.org/10.1017/s1446788700031670.

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AbstractWe prove that in a non-isotropic Euclidean space, homogeneous Lipschitz spaces of distributions, defined in terms of (generalized) Weierstrass integrals, can be characterized by means of higher order difference operators.

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48

Vergallo, Pierandrea, and Raffaele Vitolo. "Homogeneous Hamiltonian operators and the theory of coverings." Differential Geometry and its Applications 75 (April 2021): 101713. http://dx.doi.org/10.1016/j.difgeo.2020.101713.

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49

Umarkhadzhiev, Salaudin Musaevich. "On elliptic homogeneous differential operators in grand spaces." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 3 (2020): 64–73. http://dx.doi.org/10.26907/0021-3446-2020-3-64-73.

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50

Cowling, Michael, Stefano Meda, and Alberto Setti. "Invariant operators on function spaces on homogeneous trees." Colloquium Mathematicum 80, no. 1 (1999): 53–61. http://dx.doi.org/10.4064/cm-80-1-53-61.

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