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J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces And Interpolation
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Book Synopsis $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation by : Harry Dym
Download or read book $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation written by Harry Dym and published by American Mathematical Soc.. This book was released on 1989 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis J-Contractive Matrix Valued Functions and Related Topics by : Damir Z. Arov
Download or read book J-Contractive Matrix Valued Functions and Related Topics written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2008-11-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.
Book Synopsis On Boundary Interpolation for Matrix Valued Schur Functions by : Vladimir Bolotnikov
Download or read book On Boundary Interpolation for Matrix Valued Schur Functions written by Vladimir Bolotnikov and published by American Mathematical Soc.. This book was released on 2006 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of interpolation problems are considered in the Schur class of $p\times q$ matrix valued functions $S$ that are analytic and contractive in the open unit disk. The interpolation constraints are specified in terms of nontangential limits and angular derivatives at one or more (of a finite number of) boundary points. Necessary and sufficient conditions for existence of solutions to these problems and a description of all the solutions when these conditions are met is given.The analysis makes extensive use of a class of reproducing kernel Hilbert spaces ${\mathcal{H (S)$ that was introduced by de Branges and Rovnyak. The Stein equation that is associated with the interpolation problems under consideration is analyzed in detail. A lossless inverse scattering problem isalso considered.
Book Synopsis Reproducing Kernel Hilbert Spaces in Probability and Statistics by : Alain Berlinet
Download or read book Reproducing Kernel Hilbert Spaces in Probability and Statistics written by Alain Berlinet and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.
Book Synopsis Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by : Daniel Alpay
Download or read book Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.
Book Synopsis Operator Theory and Analysis by : H. Bart
Download or read book Operator Theory and Analysis written by H. Bart and published by Springer Science & Business Media. This book was released on 2001-01-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: On November 12-14, 1997 a workshop was held at the Vrije Universiteit Amsterdam on the occasion of the sixtieth birthday ofM. A. Kaashoek. The present volume contains the proceedings of this workshop. The workshop was attended by 44 participants from all over the world: partici pants came from Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, The Netherlands, South Africa, Switzerland, Ukraine and the USA. The atmosphere at the workshop was very warm and friendly. There where 21 plenary lectures, and each lecture was followed by a lively discussion. The workshop was supported by: the Vakgroep Wiskunde of the Vrije Univer siteit, the department of Mathematics and Computer Science of the Vrije Univer siteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics of the Erasmus University Rotterdam. The organizers would like to take this opportunity to express their gratitude for the support. Without it the workshop would not have been so successful as it was. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Photograph of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Curriculum Vitae of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Publications of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix l. Gohberg Opening Address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi H. Bart, A. C. M. Ran and H. I. Woerdeman Personal Reminiscences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv V. Adamyan and R. Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Conditions for the Separation of Spectral Components . . . . . . . 4 3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Book Synopsis Topics in Matrix and Operator Theory by : H. Bart
Download or read book Topics in Matrix and Operator Theory written by H. Bart and published by Birkhäuser. This book was released on 2013-11-22 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Fifth International Colloquium on Differential Equations by : D. Bainov
Download or read book Proceedings of the Fifth International Colloquium on Differential Equations written by D. Bainov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Proceedings of the Fifth International Colloquium on Differential Equations".
Book Synopsis Probability, Geometry and Integrable Systems by : Mark Pinsky
Download or read book Probability, Geometry and Integrable Systems written by Mark Pinsky and published by Cambridge University Press. This book was released on 2008-03-17 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.
Book Synopsis Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations by : Damir Z. Arov
Download or read book Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2012-09-13 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essentially self-contained treatment ideal for mathematicians, physicists or engineers whose research is connected with inverse problems.
Book Synopsis Time-Varying Systems and Computations by : Patrick DeWilde
Download or read book Time-Varying Systems and Computations written by Patrick DeWilde and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Matrix and Operator Valued Functions by : I. Gohberg
Download or read book Matrix and Operator Valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers on different aspects of operator theory and complex analysis, covering the recent achievements of the Odessa-Kharkov school, where Potapov was very active. The book appeals to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.
Book Synopsis Reproducing Kernel Spaces and Applications by : Daniel Alpay
Download or read book Reproducing Kernel Spaces and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition. The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Book Synopsis Orthogonal Rational Functions by : Adhemar Bultheel
Download or read book Orthogonal Rational Functions written by Adhemar Bultheel and published by Cambridge University Press. This book was released on 1999-02-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.
Book Synopsis Linear Algebra in Action by : Harry Dym
Download or read book Linear Algebra in Action written by Harry Dym and published by American Mathematical Society. This book was released on 2023-07-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.
Book Synopsis Matrix Completions, Moments, and Sums of Hermitian Squares by : Mihály Bakonyi
Download or read book Matrix Completions, Moments, and Sums of Hermitian Squares written by Mihály Bakonyi and published by Princeton University Press. This book was released on 2011-07-18 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.
Book Synopsis Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations by : Wolfgang Arendt
Download or read book Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2012-06-15 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains a collection of original research articles and expository contributions on recent developments in operator theory and its multifaceted applications. They cover a wide range of themes from the IWOTA 2010 conference held at the TU Berlin, Germany, including spectral theory, function spaces, mathematical system theory, evolution equations and semigroups, and differential and difference operators. The book encompasses new trends and various modern topics in operator theory, and serves as a useful source of information to mathematicians, scientists and engineers.
