Relevant bibliographies by topics / Vector valued functions

Academic literature on the topic 'Vector valued functions'

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Published: 4 June 2021
Last updated: 25 July 2024

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Journal articles on the topic "Vector valued functions"

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Matkowski, Janusz. "Mean-value theorem for vector-valued functions." Mathematica Bohemica 137, no. 4 (2012): 415–23. http://dx.doi.org/10.21136/mb.2012.142997.

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Carmichael, Richard D. "Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values." Axioms 12, no. 11 (November 6, 2023): 1036. http://dx.doi.org/10.3390/axioms12111036.

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Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.
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Bonet, J., E. Jordá, and M. Maestre. "Vector-valued meromorphic functions." Archiv der Mathematik 79, no. 5 (November 2002): 353–59. http://dx.doi.org/10.1007/pl00012457.

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Bagheri-Bardi, G. A. "Vector-valued measurable functions." Topology and its Applications 252 (February 2019): 1–8. http://dx.doi.org/10.1016/j.topol.2018.11.002.

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He, Jianxun, and Shouyou Huang. "Constructions of Vector-Valued Filters and Vector-Valued Wavelets." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/130939.

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Leta =(a1,a2,…,am)∈ℂmbe anm-dimensional vector. Then, it can be identified with anm×mcirculant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.
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Domański, Paweł, and Michael Langenbruch. "Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions." Publications of the Research Institute for Mathematical Sciences 44, no. 4 (2008): 1097–142. http://dx.doi.org/10.2977/prims/1231263781.

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Roy, S. K., and N. D. Chakraborty. "Integration of vector-valued functions with respect to an operator-valued measure." Czechoslovak Mathematical Journal 36, no. 2 (1986): 198–209. http://dx.doi.org/10.21136/cmj.1986.102084.

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Cichoń, Dariusz, and Harold S. Shapiro. "Toeplitz operators in Segal-Bargmann spaces of vector-valued functions vector-valued functions." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 275. http://dx.doi.org/10.7146/math.scand.a-14424.

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We discuss new results concerning unbounded Toeplitz operators defined in Segal-Bargmann spaces of (vector-valued) functions, i.e. the space of all entire functions which are square summable with respect to the Gaussian measure in $\mathrm{C}^n$. The problem of finding adjoints of analytic Toeplitz operators is solved in some cases. Closedness of the range of analytic Toeplitz operators is studied. We indicate an example of an entire function inducing a Toeplitz operator, for which the space of polynomials is not a core though it is contained in its domain.
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Carmichael, Richard D. "Cauchy Integral and Boundary Value for Vector-Valued Tempered Distributions." Axioms 11, no. 8 (August 10, 2022): 392. http://dx.doi.org/10.3390/axioms11080392.

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Using the historically general growth condition on scalar-valued analytic functions, which have tempered distributions as boundary values, we show that vector-valued analytic functions in tubes TC=Rn+iC obtain vector-valued tempered distributions as boundary values. In a certain vector-valued case, we study the structure of this boundary value, which is shown to be the Fourier transform of the distributional derivative of a vector-valued continuous function of polynomial growth. A set of vector-valued functions used to show the structure of the boundary value is shown to have a one–one and onto relationship with a set of vector-valued distributions, which generalize the Schwartz space DL2′(Rn); the tempered distribution Fourier transform defines the relationship between these two sets. By combining the previously stated results, we obtain a Cauchy integral representation of the vector-valued analytic functions in terms of the boundary value.
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Banakh, Iryna, Taras Banakh, and Kaori Yamazaki. "Extenders for vector-valued functions." Studia Mathematica 191, no. 2 (2009): 123–50. http://dx.doi.org/10.4064/sm191-2-2.

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Dissertations / Theses on the topic "Vector valued functions"

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Barclay, Steven John. "Banach spaces of analytic vector-valued functions." Thesis, University of Leeds, 2007. http://etheses.whiterose.ac.uk/167/.

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The main theme of the thesis is the study of continuity and approximation problems, involving matrix-valued and vector-valued Hardy spaces on the unit disc ID and its boundary T in the complex plane. The first part of the thesis looks at the factorization of square matrix-valued boundary functions, beginning with spectral factorization in Chapter 2. Then ideas involving approximations with inner and outer functions are used to solve a matrix analogue of the Douglas-Rudin problem in Chapter 3. In both cases, considerable considerable extra difficulties are created by the noncommutativity of matrix multiplication. More specifically, we show that the matrix spectral factorization mapping is sequentially continuous from LP to H2p (where 1
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Hossain, M. Ayub. "The stochastic preference relations for vector valued attributes /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487331541711522.

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Kerr, Robert. "Toeplitz products and two-weight inequalities on spaces of vector-valued functions." Thesis, University of Glasgow, 2011. http://theses.gla.ac.uk/2469/.

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This thesis is concerned with operators on certain vector-valued function spaces. Namely, Bergman spaces of \mathbb{C}^n$-valued functions and L^2(\mathbb{R},\mathbb{C}^n,V)$, where $V$ is a matrix weight. We will study products of Toeplitz operators on the vector Bergman space $L^2_a(\mathbb{C}^n)$. We also study various operators, including the dyadic shift and the Hilbert transform, between $L^2(\mathbb{R},\mathbb{C}^n,V)$ and $L^2(\mathbb{R},\mathbb{C}^n,U)$. These function spaces are generalizations of normed vector spaces of functions which take values in $\mathbb{C}$. The thesis is split into two distinct areas of function space theory: analytic function spaces and harmonic analysis. There is, however, a common theme of matrix weights, particularly the reverse Hölder condition on matrix weights and a generalization of the $A_p$ conditions on matrix weights for $p=2$ and $p=\infty$.
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Wahlberg, Patrik. "On time-frequency analysis and pseudo-differential operators for vector-valued functions." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2336.

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This thesis treats different aspects of time-frequency analysis and pseudodifferential operators, with particular emphasis on techniques involving vector-valued functions and operator-valued symbols. The vector (Banach) space is either motivated by an application as in Paper I, where it is a space of stochastic variables, or is part of a general problem as in Paper II, or arises naturally from problems for scalar-valued operators and function spaces, as in Paper V. Paper III and IV fall outside this framework and treats algebraic aspects of time-frequency analysis and pseudodifferential operators for scalar-valued symbols and functions that are members of modulation spaces. Paper IV builds upon Paper III and applies the results to a filtering problem for second-order stochastic processes. Paper I treats the Wigner distribution of a Gaussian weakly harmonizable stochastic process defned on Rd. Paper II extends recent continuity results for pseudodifferential and localization operators, with symbols in modulation spaces, to the vector/operator-framework, where the vector space is a Hilbert or a Banach space. In Paper III we give algebraic results for the Weyl product acting on modulation spaces. We give suffcient conditions for a weighted modulation space to be an algebra under theWeyl product, and we also give necessary conditions for unweighted modulation spaces. In Paper IV we discretize the results of Paper III by means of a Gabor frame delined by a Gaussian function. Finally, Paper V deals with pseudodifferential operators with symbols that are almost periodic in the first variable. We show that such operators may be transformed to Fourier multiplier operators with operator- valued symbols such that the transformation preserves positivity and operator composition.
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Oliver, Vendrell Roc. "Hankel operators on vector-valued Bergman spaces." Doctoral thesis, Universitat de Barcelona, 2017. http://hdl.handle.net/10803/471520.

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The main goal of this work is to study vector-valued Bergman spaces and to obtain the weak factorization of these spaces. In order to do that we need to study small Hankel operators with operator-valued holomorphic symbols. We also study the big Hankel operator acting on vector-valued Bergman spaces. In Chapter 1 we collect all the previous results and notations needed to follow the rest of the manuscript. More concretely, some of the topics covered in this chapter are the Bochner integral, the integral for vector-valued functions appearing first in Bochner; the Bergman metric, results of the metric used in Bn; harmonic and subharmonic function; basic notions of differentiation, where the differential operators R(a, t) are presented which is important in the next chapters and in the final section we recall some topics on Banach spaces, as the Rademacher type and cotype of a Banach space and some other related results. Having all that in mind, in Chapter 2, the vector-valued Bergman spaces are presented. The vector-valued Bloch type spaces play a similar role and therefore we dedícate one full chapter to these spaces. Chapter 3 is devoted to present and characterize the vector-valued Bloch type spaces. Since we mention Hankel operators, in Chapter 4 we prove the characterization of the boundedness of the small Hankel operator with analytic operator-valued symbols between vector-valued Bergman spaces (of different type). We explain what this means in the following. Another very important consequence of the boundedness of the small Hankel operator between vector-valued Bergman spaces is shown in Chapter 5. We establish the weak factorization of the vector-valued Bergman spaces. Factorization of analytic functions is a very big topic and many people worked on it during many years and it is known to have many applications. Therefore, in Chapter 6 we fully characterize the boundedness of the big Hankel operator on vector-valued Bergman spaces in terms of its operator-valued holomorphic symbol for all cases of p > 1 and q > 1, and so we solve and generalize the previous problem. Finally, in Chapter 7 we discuss some open problems we have not been able to solve, as well as some other interesting problems in the same line as this work in order to look on the future.
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Vu, Anh Tuan [Verfasser]. "Lipschitz properties of vector- and set-valued functions with applications / Anh Tuan Vu." Halle, 2018. http://d-nb.info/1153007819/34.

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Juan, Huguet Jordi. "Iterates of differential operators and vector valued functions on non quasi analytic classes." Doctoral thesis, Universitat Politècnica de València, 2011. http://hdl.handle.net/10251/9401.

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En el año 1960 Komatsu introdujo ciertas clases de funciones infinitamente derivables definidas mediante estimaciones del crecimiento de los sucesivos iterados de un operador en derivadas parciales cuando estudiaba propiedades de regularidad de las soluciones de ciertas ecuaciones en derivadas parciales. Esta línea de investigación ha sido muy activa hasta la actualidad a través de los trabajos de muchos autores. Destacamos, entre otros, Bolley, Camus, Kotake, Langenbruch, Métivier, Narasimhan, Newberger, Rodino, Zanghirati y Zielezny. Toda esta bibliografía involucra el llamado problema de los iterados que consiste, grosso modo, en caracterizar las funciones de una cierta clase en términos del comportamiento de los iterados de un operador previamente fijado. En la primera parte de esta tesis seguimos con la investigación mencionada antes en un contexto más general: clases no casi analíticas de funciones ultradiferenciables en el sentido de Braun, Meise y Taylor. El estudio de estas clases no casi analíticas es una área de investigación muy activa debido a sus aplicaciones a la teoría de operadores en derivadas parciales: destacamos entre otros el trabajo de Bonet, Braun, Domanski, Fernández, Frerick, Galbis, Taylor y Vogt. En el Capítulo 1 introducimos estas clases y enunciamos las propiedados que utilizaremos a lo largo de esta tesis. En el Capítulo 2 definimos las clases no casi analíticas con respecto a los iterados de un operador en derivadas parciales P(D) y estudiamos sus propiedades topológicas como la completitud y la nuclearidad. En particular, demostramos que estas clases son un espacio localmente convexo completo si y sólo si el operador P(D) es hipoelíptico y vemos que en tal caso son además un espacio nuclear. A continuación, demostramos que estas clases verifican un teorema de tipo Paley-Wiener. En el Capítulo 3 tenemos como objetivo obtener resultados sobre el problema de los iterados en clases no casi analíticas. Generalizamos varios resultados de Newberger, Zielezny, Métivier y Komatsu y damos caracterizaciones de cuándo una clase no casi analítica definida en términos de los iterados de un operador coincide con una clase no casi analítica según Braun, Meise y Taylor. Toda la investigación que se había hecho sobre espacios de funciones definidos por iterados de operadores se había centrado en clases de tipo Roumieu. Sin embargo, demostramos que los resultados dados en los Capítulos 2 y 3 también son válidos para clases de tipo Beurling. En el año 1990, Langenbruch y Voigt demostraron que todo espacio de Fréchet formado por distribuciones que sea invariante bajo la acción de un operador hipoelíptico está continuamente incluido en C¥. En el capítulo 4 introducimos los operadores ultradiferenciales e investigamos extensiones del resultado de Langenbruch y Voigt al contexto ultradiferenciable. El nuevo concepto de espacio de Fréchet (w, P(D))-estable involucra a los iterados de P(D) mediante una condición de equicontinuidad y nos permite mostrar la relación de este tipo de resultados con el problema de los iterados. La segunda parte de esta tesis se centra en el estudio de funciones con valores vectoriales en un espacio localmente convexo.
Juan Huguet, J. (2011). Iterates of differential operators and vector valued functions on non quasi analytic classes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/9401
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Martin, C. Wayne. "Quantization using permutation codes with a uniform source /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/martinc/cwaynemartin.pdf.

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De, Kock Mienie. "Absolute continuity and on the range of a vector measure." [Kent, Ohio] : Kent State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=kent1216134542.

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Thesis (Ph.D.)--Kent State University, 2008.
Title from PDF t.p. (viewed Jan. 26, 2010). Advisor: Joseph Diestel. Keywords: absolute continiuty, range of a vector measure. Includes bibliographical references (p. 40-41).
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Batista, Leandro Candido. "Teoria isomorfa dos espaços de Banach C0(K,X)." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-17072013-113811/.

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Para um espaço localmente compacto de Hausdorff K e um espaço de Banach X, denotamos por C0(K,X) o espaço de todas as funções a valores em X contínuas sobre K que se anulam no infinito, munido da norma do supremo. No espírito do clássico teorema de Banach-Stone 1937, estabelecemos que se C0(K1,X) é isomorfo a C0(K2,X), onde X é um espaço de Banach de cotipo finito e tal que X é separável ou X* tem a propriedade de Radon-Nikodým, então ou K1 e K2 são ambos finitos ou K1 e K2 tem a mesma cardinalidade. Trata-se de uma extensão vetorial de um resultado de Cengiz 1978, o caso escalar X = R ou X = C. Demonstramos também que se K1 e K2 são intervalos compactos de ordinais e X é um espaço de Banach de cotipo finito, então a existência de um isomorfismo T de C(K1,X) em C(K2,X) com ||T||||T-1|| < 3 implica que uma certa soma topológica finita de K1 é homeomorfa a alguma soma topológica finita de K2. Mais ainda, se Xn não contém subespaço isomorfo a Xn+1 para todo n ∈ N, então K1 é homeomorfo a K2. Em outras palavras, obtemos um teorema tipo Banach-Stone vetorial que é uma extensão de um teorema de Gordon de 1970 e ao mesmo tempo uma extensão de um teorema de Behrends e Cambern de 1988. Mostramos que se existe um isomorfismo T de C(K1) em um subespaço de C(K2,X) com ||T||||T-1|| < 3, então a cardinalidade do α-ésimo derivado de K2 ou é finita ou é maior do que a cardinalidade do α-ésimo derivado de K1, para todo ordinal α. Em seguida, seja n um inteiro positivo, Γ um conjunto infinito munido da topologia discreta e X um espaço de Banach de cotipo finito. Estabelecemos que se o n-ésimo derivado de K for não vazio, então a distância de Banach-Mazur entre C0(K,X) e C0(Γ,X) é maior ou igual a 2n + 1. Também demonstramos que para quaisquer inteiros positivos n e k, a distância de Banach-Mazur entre C([1,ωnk],X) e C0(N,X) é exatamente 2n+1. Estes resultados fornecem extensões vetoriais para alguns teoremas de Cambern de 1970. Para um ordinal enumerável α, denotando por C(α) o espaço de Banach das funções contínuas no intervalo de ordinal [1, α], obtemos cotas superiores H(n, k) e cotas inferiores G(n, k) para as distâncias de Banach-Mazur entre os espaços C(ω) e C(ωnk), 1 < n, k < ω, verificando H(n, k) - G(n, k) < 2. Estas estimativas fornecem uma resposta para uma questão de Bessaga e Peczynski de 1960 sobre as distâncias de Banach-Mazur entre C(ω) e cada um dos espaços C(α), ω<α<ωω.
For a locally compact Hausdorff space K and a Banach space X, we denote by C0(K,X) the space of X-valued continuous functions on K which vanish at infinity, endowed with the supremum norm. In the spirit of the classical 1937 Banach-Stone theorem, we prove that if C0(K1,X) is isomorphic to C0(K2,X), where X is a Banach space having finite cotype and such that X is separable or X* has the Radon-Nikodým property, then either K1 and K2 are finite or K1 and K2 have the same cardinality. It is a vector-valued extension of a 1978 Cengiz result, the scalar case X = R or X = C. We also prove that if K1 and K2 are compact ordinal spaces and X is Banach space having finite cotype, then the existence of an isomorphism T from C(K1,X) onto C(K2,X) with ||T||||T-1|| < 3 implies that some finite topological sum of K1 is homeomorphic to some finite topological sum of K2. Moreover, if Xn contains no subspace isomorphic to Xn+1 for every n ∈ N, then K1 is homeomorphic to K2. In other words, we obtain a vector-valued Banach-Stone theorem which is an extension of a 1970 Gordon theorem and at same time an improvement of a 1988 Behrends and Cambern theorem. We show that if there is an embedding T of a C(K1) into C(K2,X) with ||T||||T-1|| < 3, then the cardinality of the α-th derivative of K2 is either finite or greater than the cardinality of the α-th derivative of K1, for every ordinal α. Next, let n be a positive integer, Γ an infinite set with the discrete topology and X is a Banach space having finite cotype. We prove that if the n-th derivative of K is not empty, then the Banach Mazur distance between C0(K,X) and C0(Γ,X) is greater than or equal to 2n + 1. Thus, we also show that for every positive integers n and k, the Banach Mazur distance between C([1,ωnk],X) and C0(N,X) is exactly 2n+1. These results provide vector-valued versions of some 1970 Cambern theorems. For a countable ordinal α, writing C(α) for the Banach space of continuous functions on the interval of ordinal [1, α], we give lower bounds H(n, k) and upper bounds G(n, k) on the Banach- Mazur distances between C(ω) and C(ωnk), 1 < n, k < ω, such that H(n, k) - G(n, k) < 2. These estimates provide an answer to a 1960 Bessaga and Peczynski question on the Banach-Mazur distances between C(ω) and each of the C(α) spaces, ω<α<ωω.
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Books on the topic "Vector valued functions"

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1957-, Mendoza José, ed. Banach spaces of vector-valued functions. Berlin: Springer, 1997.

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Hu, Chuang-gan. Vector-valued functions and their applications. Dordrecht: Kluwer Academic Publishers, 1992.

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Cembranos, Pilar, and José Mendoza. Banach Spaces of Vector-Valued Functions. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0096765.

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Hu, Chuang-Gan, and Chung-Chun Yang. Vector-Valued Functions and their Applications. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8030-4.

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Valéry, Covachev, ed. Complex vector functional equations. Singapore: World Scientific, 2001.

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United States. National Aeronautics and Space Administration., ed. Rational approximations from power series of vector-valued meromorphic functions. [Washington, DC: National Aeronautics and Space Administration, 1992.

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S, Kutateladze S., ed. Vektornai͡a︡ dvoĭstvennostʹ i ee prilozhenii͡a︡. Novosibirsk: Izd-vo "Nauka," Sibirskoe otd-nie, 1985.

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Kusraev, A. G. Vektornai︠a︡ dvoĭstvennostʹ i ee prilozhenii︠a︡. Novosibirsk: Nauka, 1985.

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service), SpringerLink (Online, ed. Operator-valued measures and integrals for cone-valued functions. Berlin: Springer, 2009.

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Zaidman, Samuel. Almost-periodic functions in abstract spaces. Boston: Pitman Advanced, 1985.

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Book chapters on the topic "Vector valued functions"

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Krantz, Steven G., and Harold Parks. "Vector-Valued Functions." In Vector Calculus, 105–206. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003304241-2.

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Vince, John. "Vector-Valued Functions." In Calculus for Computer Graphics, 209–15. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5466-2_12.

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Sinha, Kalyan B., and Sachi Srivastava. "Vector-Valued Functions." In Texts and Readings in Mathematics, 1–19. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-4864-7_1.

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Pao, Karen, and Frederick Soon. "Vector-Valued Functions." In Student’s Guide to Basic Multivariable Calculus, 73–88. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-4300-5_4.

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Vince, John. "Vector-Valued Functions." In Calculus for Computer Graphics, 225–32. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11376-6_12.

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Dym, Harry. "Vector-valued functions." In Graduate Studies in Mathematics, 315–36. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/gsm/078/14.

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Vince, John. "Vector-Valued Functions." In Calculus for Computer Graphics, 249–59. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28117-4_12.

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Dineen, Seán. "Vector Valued Differentiation." In Functions of Two Variables, 123–29. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-3250-1_16.

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Hu, Chuang-Gan, and Chung-Chun Yang. "Vector-Valued Analysis." In Vector-Valued Functions and their Applications, 94–150. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8030-4_3.

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Vince, John. "Differentiating Vector-Valued Functions." In Vector Analysis for Computer Graphics, 53–65. London: Springer London, 2021. http://dx.doi.org/10.1007/978-1-4471-7505-6_5.

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Conference papers on the topic "Vector valued functions"

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Goldenbaum, Mario, Holger Boche, and Slawomir Stanczak. "On analog computation of vector-valued functions in clustered wireless sensor networks." In 2012 46th Annual Conference on Information Sciences and Systems (CISS). IEEE, 2012. http://dx.doi.org/10.1109/ciss.2012.6310783.

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Ammanouil, Rita, Andre Ferrari, Cedric Richard, and Jean-Yves Tournere. "Spatial regularization for nonlinear unmixing of hyperspectral data with vector-valued kernel functions." In 2016 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2016. http://dx.doi.org/10.1109/ssp.2016.7551845.

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Carniello, Rafael A. F., Wington L. Vital, and Marcos Eduardo Valle. "Universal Approximation Theorem for Tessarine-Valued Neural Networks." In Encontro Nacional de Inteligência Artificial e Computacional. Sociedade Brasileira de Computação - SBC, 2021. http://dx.doi.org/10.5753/eniac.2021.18256.

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The universal approximation theorem ensures that any continuous real-valued function defined on a compact subset can be approximated with arbitrary precision by a single hidden layer neural network. In this paper, we show that the universal approximation theorem also holds for tessarine-valued neural networks. Precisely, any continuous tessarine-valued function can be approximated with arbitrary precision by a single hidden layer tessarine-valued neural network with split activation functions in the hidden layer. A simple numerical example, confirming the theoretical result and revealing the superior performance of a tessarine-valued neural network over a real-valued model for interpolating a vector-valued function, is presented in the paper.
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Plattner, Alain, and Frederik J. Simons. "A spatiospectral localization approach for analyzing and representing vector-valued functions on spherical surfaces." In SPIE Optical Engineering + Applications, edited by Dimitri Van De Ville, Vivek K. Goyal, and Manos Papadakis. SPIE, 2013. http://dx.doi.org/10.1117/12.2024703.

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Guo, Zehui, Tomohisa Hayakawa, and Yuyue Yan. "Stability and Stabilization of Nash Equilibrium for Noncooperative Systems With Vector-Valued Payoff Functions." In 2023 62nd IEEE Conference on Decision and Control (CDC). IEEE, 2023. http://dx.doi.org/10.1109/cdc49753.2023.10384265.

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Alexander, Michael J., James T. Allison, Panos Y. Papalambros, and David J. Gorsich. "Constraint Management of Reduced Representation Variables in Decomposition-Based Design Optimization." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28788.

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In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC), it is sometimes necessary to use reduced dimensionality representations to approximate functions of large dimensionality whose values need to be exchanged among subproblems. The reduced representation variables may not be physically meaningful, and it can become challenging to constrain them properly and define the model validity region. For example, in coordination strategies like ATC, representing vector-valued coupling variables with improperly constrained reduced representation variables can lead to poor performance or convergence failure. This paper examines two approaches for constraining effectively the model validity region of reduced representation variables based on proper orthogonal decomposition: a penalty value-based heuristic and a support vector domain description. An ATC application on electric vehicle design helps to illustrate the concepts discussed.
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Silverman, M. P. "Comparison of coherence properties of thermal electrons and blackbody radiation." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.tui4.

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The profound distinctions between photon and Fermion optics appear in the second-order coherence properties of the particle field.1 Particularly significant are blackbody radiation2 and thermal electron fields; the correlation functions are uniquely specified by temperature θ and chemical potential u. Differences in the second-order coherence arise principally from considerations of (a) particle conservation (photons are not conserved; electron conservation is rigorous and tantamount to charge conservation); (b) tensorial character of the fields (electromagnetic fields are vector-valued; electron fields are spinor-valued); (c) quantum statistics (photons and electrons are subject to Bose-Einstein and Fermi-Dirac statistics, respectively).
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Chiozzi, A. "Extended virtual element method for elliptic problems with singularities and discontinuities in mechanics." In AIMETA 2022. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902431-39.

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Abstract. Drawing inspiration from the extended finite element method (X-FEM), we propose for two-dimensional elastic fracture problems, an extended virtual element method (X-VEM). In the X-VEM, we extend the standard virtual element space with the product of vector-valued virtual nodal shape functions and suitable enrichment fields, which reproduce the singularities of the exact solution. We define an extended projection operator that maps functions in the extended virtual element space onto a set spanned by the space of linear polynomials augmented with the enrichment fields. Several numerical examples are adopted to illustrate the convergence and accuracy of the proposed method, for both quadrilateral and general polygonal meshes.
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CHRISTODOULIDES, Y. T. "ASYMPTOTICS OF GENERALIZED VALUE DISTRIBUTION FOR HERGLOTZ FUNCTIONS." In Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277723_0005.

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Benedetto, John J., and Jeffrey J. Donatelli. "Frames and a vector-valued ambiguity function." In 2008 42nd Asilomar Conference on Signals, Systems and Computers. IEEE, 2008. http://dx.doi.org/10.1109/acssc.2008.5074350.

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Reports on the topic "Vector valued functions"

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Liu, Jing, Channing Arndt, and Thomas Hertel. Parameter Estimation and Measures of Fit in A Global, General Equilibrium Model. GTAP Working Paper, March 2003. http://dx.doi.org/10.21642/gtap.wp24.

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Computable General Equilibrium (CGE) models have been widely used for quantitative analysis of global economic issues. However, CGE models are frequently criticized for resting on weak empirical foundations. This paper builds on recent work in macro-econometric estimation, developing an approach to parameter estimation for a widely employed global CGE model, the Global Trade Analysis Project (GTAP) model. An approximate likelihood function is developed and the set of optimum elasticity values is obtained by maximizing this approximate likelihood function in the context of a back casting exercise. In addition, two statistical tests are performed. The first of these tests compares the standard GTAP elasticity vector with the estimated trade elasticity vector. It rejects the null hypothesis of equality between the two sets of trade elasticities. The second test examines the widely maintained hypothesis known as the “rule of two”, by which the elasticity of substitution across imports by sources is set equal to twice the elasticity of substitution between domestic goods and imports. We fail to reject this common rule of thumb. We conclude that there is much to be gained by nesting CGE models within an estimation framework as this opens the way for formal evaluation of model performance and parameterization.
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Huntley, D., D. Rotheram-Clarke, R. Cocking, J. Joseph, and P. Bobrowsky. Current research on slow-moving landslides in the Thompson River valley, British Columbia (IMOU 5170 annual report). Natural Resources Canada/CMSS/Information Management, 2022. http://dx.doi.org/10.4095/331175.

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Interdepartmental Memorandum of Understanding (IMOU) 5170 between Natural Resources Canada (NRCAN), the Geological Survey of Canada (GSC) and Transport Canada Innovation Centre (TC-IC) aims to gain new insight into slow-moving landslides, and the influence of climate change, through testing conventional and emerging monitoring technologies. IMOU 5107 focuses on strategically important sections of the national railway network in the Thompson River valley, British Columbia (BC), and the Assiniboine River valley along the borders of Manitoba (MN) and Saskatchewan (SK). Results of this research are applicable elsewhere in Canada (e.g., the urban-rural-industrial landscapes of the Okanagan Valley, BC), and around the world where slow-moving landslides and climate change are adversely affecting critical socio-economic infrastructure. Open File 8931 outlines landslide mapping and changedetection monitoring protocols based on the successes of IMOU 5170 and ICL-IPL Project 202 in BC. In this region, ice sheets, glaciers, permafrost, rivers and oceans, high relief, and biogeoclimatic characteristics contribute to produce distinctive rapid and slow-moving landslide assemblages that have the potential to impact railway infrastructure and operations. Bedrock and drift-covered slopes along the transportation corridors are prone to mass wasting when favourable conditions exist. In high-relief mountainous areas, rapidly moving landslides include rock and debris avalanches, rock and debris falls, debris flows and torrents, and lahars. In areas with moderate to low relief, rapid to slow mass movements include rockslides and slumps, debris or earth slides and slumps, and earth flows. Slow-moving landslides include rock glaciers, rock and soil creep, solifluction, and lateral spreads in bedrock and surficial deposits. Research efforts lead to a better understanding of how geological conditions, extreme weather events and climate change influence landslide activity along the national railway corridor. Combining field-based landslide investigation with multi-year geospatial and in-situ time-series monitoring leads to a more resilient railway national transportation network able to meet Canada's future socioeconomic needs, while ensuring protection of the environment and resource-based communities from landslides related to extreme weather events and climate change. InSAR only measures displacement in the east-west orientation, whereas UAV and RTK-GNSS change-detection surveys capture full displacement vectors. RTK-GNSS do not provide spatial coverage, whereas InSAR and UAV surveys do. In addition, InSAR and UAV photogrammetry cannot map underwater, whereas boat-mounted bathymetric surveys reveal information on channel morphology and riverbed composition. Remote sensing datasets, consolidated in a geographic information system, capture the spatial relationships between landslide distribution and specific terrain features, at-risk infrastructure, and the environmental conditions expected to correlate with landslide incidence and magnitude. Reliable real-time monitoring solutions for critical railway infrastructure (e.g., ballast, tracks, retaining walls, tunnels, and bridges) able to withstand the harsh environmental conditions of Canada are highlighted. The provision of fundamental geoscience and baseline geospatial monitoring allows stakeholders to develop robust risk tolerance, remediation, and mitigation strategies to maintain the resilience and accessibility of critical transportation infrastructure, while also protecting the natural environment, community stakeholders, and Canadian economy. We propose a best-practice solution involving three levels of investigation to describe the form and function of the wide range of rapid and slow-moving landslides occurring across Canada that is also applicable elsewhere. Research activities for 2022 to 2025 are presented by way of conclusion.
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