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.
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 :
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 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.
J Contractive Matrix Valued Functions And Related Topics
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Author : Damir Z. Arov
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-06
J Contractive Matrix Valued Functions And Related Topics written by Damir Z. Arov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-06 with Mathematics categories.
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.
Schur Functions Operator Colligations And Reproducing Kernel Pontryagin Spaces
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Schur Functions Operator Colligations And Reproducing Kernel Pontryagin Spaces 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.
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.
Interpolation Schur Functions And Moment Problems
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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-22
Interpolation Schur Functions And Moment Problems written by Daniel Alpay 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 2006-06-22 with Mathematics categories.
Schur analysis originated with an 1917 article which associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients, often named reflection coefficients in signal processing. This volume comprises seven essays dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
Extension Of Positive Definite Distributions And Maximum Entropy
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Author : Jean-Pierre Gabardo
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Extension Of Positive Definite Distributions And Maximum Entropy written by Jean-Pierre Gabardo 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.
In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
Characteristic Functions Scattering Functions And Transfer Functions
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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-12
Characteristic Functions Scattering Functions And Transfer Functions written by Daniel Alpay 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 2010-01-12 with Mathematics categories.
Transfer functions and characteristic functions proved to be key in operator theory and system theory. Moshe Livic played a major role in developing these functions, and this book of papers dedicated to his memory covers a wide variety of topics in the field.
Matrix Completions Moments And Sums Of Hermitian Squares
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Author : Mihály Bakonyi
language : en
Publisher: Princeton University Press
Release Date : 2011-07-18
Matrix Completions Moments And Sums Of Hermitian Squares written by Mihály Bakonyi and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Mathematics categories.
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.
Recent Developments In Operator Theory Mathematical Physics And Complex Analysis
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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2023-04-11
Recent Developments In Operator Theory Mathematical Physics And Complex Analysis written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-11 with Mathematics categories.
This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.
An Advanced Complex Analysis Problem Book
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2015-11-13
An Advanced Complex Analysis Problem Book 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 2015-11-13 with Mathematics categories.
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.