J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces And Interpolation

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J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces And Interpolation

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Author : Harry Dym
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces And Interpolation written by Harry Dym and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.

Matrix And Operator Valued Functions

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Author : I. Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Matrix And Operator Valued Functions written by I. Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is dedicated to the memory of an outstanding mathematician and personality, Vladimir Petrovich Potapov, who made important contributions to and exerted considerable influence in the areas of operator theory, complex analysis and their points of juncture. The book commences with insightful biographical material, and then presents a collection of papers on different aspects of operator theory and complex analysis covering those recent achievements of the Odessa-Kharkov school in which Potapov was very active. The papers deal with interrelated problems and methods. The main topics are the multiplicative structure of contractive matrix and operator functions, operators in spaces with indefinite scalar products, inverse problems for systems of differential equations, interpolation and approximation problems for operator and matrix functions. The book will appeal to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.

Topics In Matrix And Operator Theory

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Author : H. Bart
language : en
Publisher: Birkhäuser
Release Date : 2013-11-22

Topics In Matrix And Operator Theory written by H. Bart and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Social Science categories.

Integral Transforms Reproducing Kernels And Their Applications

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Author : Saburou Saitoh
language : en
Publisher: CRC Press
Release Date : 2020-11-26

Integral Transforms Reproducing Kernels And Their Applications written by Saburou Saitoh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.

The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.

Geometric Analysis And Function Spaces

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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Geometric Analysis And Function Spaces written by Steven George Krantz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.

Banach Spaces Of Analytic Functions And Absolutely Summing Operators

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Author : Aleksander Pełczyński
language : en
Publisher: American Mathematical Soc.
Release Date : 1977-12-31

Banach Spaces Of Analytic Functions And Absolutely Summing Operators written by Aleksander Pełczyński and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-12-31 with Mathematics categories.

This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.

Inverse Problems And Nonlinear Evolution Equations

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Author : Alexander L. Sakhnovich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31

Inverse Problems And Nonlinear Evolution Equations written by Alexander L. Sakhnovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.

This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

Time Varying Systems And Computations

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Author : Patrick DeWilde
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Time Varying Systems And Computations written by Patrick DeWilde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.

Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari able s or z and it is analytic in a large part of the complex plane. Many important prop erties of the system for which it is a transfer function are related to its analytic prop erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.

Operator Theory And Complex Analysis

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Author : T. Ando
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Operator Theory And Complex Analysis written by T. Ando and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.

Reproducing Kernel Spaces And Applications

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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Reproducing Kernel Spaces And Applications written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

20. Pattern recognition and statistical learning theory (the theory of support vector machines). See [40], [58]. In this last volume we refer in particular to the papers [63] and [64]. Since this topic is maybe less known to the operator theory community we mention that the support vector method is a general approach to function estimation problems. See [63, p. 26]. We note that the above list and the given references are by no way exhaustive. We refer to the first section of the paper of S. Saitoh in the present volume for another (and mainly different) list of topics where reproducing kernel spaces appear. Quite often a given question is best understood in a reproducing kernel Hilbert space (for instance when using Cauchy's formula in the Hardy space H ) 2 and one finds oneself as Mr Jourdain of Moliere' Bourgeois Gentilhomme speaking Prose without knowing it [48, p. 51]: Par ma foil il y a plus de quarante ans que je dis de la prose sans que l j'en susse rien.