The Schur Algorithm Reproducing Kernel Spaces And System Theory

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The Schur Algorithm, Reproducing Kernel Spaces and System Theory

Daniel Alpay
The Schur Algorithm Reproducing Kernel Spaces and System Theory Book PDF

Author : Daniel Alpay
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 47,5 Mb
Release : 2001
Category : Computers
ISBN : 0821821555

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The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay Pdf

The class of Schur functions consists of analytic functions on the unit disk that are bounded by $1$. The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering. In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Societe Mathematique de France. Translated by Stephen S. Wilson.

System Theory, the Schur Algorithm and Multidimensional Analysis

Daniel Alpay,Victor Vinnikov
System Theory the Schur Algorithm and Multidimensional Analysis Book PDF

Author : Daniel Alpay,Victor Vinnikov
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 52,7 Mb
Release : 2007-06-28
Category : Mathematics
ISBN : 9783764381370

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System Theory, the Schur Algorithm and Multidimensional Analysis by Daniel Alpay,Victor Vinnikov Pdf

This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Reproducing Kernel Spaces and Applications

Daniel Alpay
Reproducing Kernel Spaces and Applications Book PDF

Author : Daniel Alpay
Publisher : Birkhäuser
Page : 355 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880770

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Reproducing Kernel Spaces and Applications by Daniel Alpay Pdf

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.

System Theory, the Schur Algorithm and Multidimensional Analysis

Daniel Alpay,Victor Vinnikov
System Theory the Schur Algorithm and Multidimensional Analysis Book PDF

Author : Daniel Alpay,Victor Vinnikov
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 53,7 Mb
Release : 2007-03-20
Category : Mathematics
ISBN : 9783764381363

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System Theory, the Schur Algorithm and Multidimensional Analysis by Daniel Alpay,Victor Vinnikov Pdf

This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo
Schur Functions Operator Colligations and Reproducing Kernel Pontryagin Spaces Book PDF

Author : Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo
Publisher : Birkhäuser
Page : 244 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889087

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Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo Pdf

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.

Theory of Reproducing Kernels and Applications

Saburou Saitoh,Yoshihiro Sawano
Theory of Reproducing Kernels and Applications Book PDF

Author : Saburou Saitoh,Yoshihiro Sawano
Publisher : Springer
Page : 452 pages
File Size : 50,7 Mb
Release : 2016-10-14
Category : Mathematics
ISBN : 9789811005305

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Theory of Reproducing Kernels and Applications by Saburou Saitoh,Yoshihiro Sawano Pdf

This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.

More Progresses in Analysis

Heinrich G. W. Begehr,Francesco Nicolosi
More Progresses in Analysis Book PDF

Author : Heinrich G. W. Begehr,Francesco Nicolosi
Publisher : World Scientific
Page : 1497 pages
File Size : 54,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812835628

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More Progresses in Analysis by Heinrich G. W. Begehr,Francesco Nicolosi Pdf

International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.

More Progresses in Analysis

Anonim
More Progresses in Analysis Book PDF

Author : Anonim
Publisher : World Scientific
Page : 1497 pages
File Size : 40,6 Mb
Release : 2009-05-12
Category : Mathematics
ISBN : 9789812835635

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More Progresses in Analysis by Anonim Pdf

International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O. Besov, V. Burenkov and R.P. Gilbert on the occasion of their anniversaries.

Studies in Memory of Issai Schur

Anthony Joseph,Anna Melnikov,Rudolf Rentschler
Studies in Memory of Issai Schur Book PDF

Author : Anthony Joseph,Anna Melnikov,Rudolf Rentschler
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200451

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Studies in Memory of Issai Schur by Anthony Joseph,Anna Melnikov,Rudolf Rentschler Pdf

This volume Studies in Memory of Issai Schur was conceived as a tribute to Schur's of his tragic end. His impact on great contributions to mathematics and in remembrance of mathematicians Representation Theory alone was so great that a significant number of Researchers (TMR) Network, in the European Community Training and Mobility Orbits, Crystals and Representation Theory, in operation during the period (1997-2002) have been occupied with what has been called Schur theory. Consequently, this volume has the additional purpose of recording some of the significant results of the network. It was furthermore appropriate that invited contributors should be amongst the speakers at the Paris Midterm Workshop of the network held at Chevaleret during 21-25 May, 2000 as well as those of the Schur Memoriam Workshop held at the Weizmann Institute, Rehovot, during 27-31 December 2000. The latter marked the sixtieth anniversary of Schur's passing and took place in the 125th year of his birth.

A Panorama of Modern Operator Theory and Related Topics

Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer
A Panorama of Modern Operator Theory and Related Topics Book PDF

Author : Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer
Publisher : Springer Science & Business Media
Page : 635 pages
File Size : 42,7 Mb
Release : 2012-02-01
Category : Mathematics
ISBN : 9783034802215

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A Panorama of Modern Operator Theory and Related Topics by Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer Pdf

This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

Palle Jorgensen,James Tian
Infinite dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory Book PDF

Author : Palle Jorgensen,James Tian
Publisher : World Scientific
Page : 253 pages
File Size : 54,6 Mb
Release : 2021-01-15
Category : Mathematics
ISBN : 9789811225796

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by Palle Jorgensen,James Tian Pdf

The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Current Trends in Operator Theory and its Applications

Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman
Current Trends in Operator Theory and its Applications Book PDF

Author : Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman
Publisher : Birkhäuser
Page : 604 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878814

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Current Trends in Operator Theory and its Applications by Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman Pdf

Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

Slice Hyperholomorphic Schur Analysis

Daniel Alpay,Fabrizio Colombo,Irene Sabadini
Slice Hyperholomorphic Schur Analysis Book PDF

Author : Daniel Alpay,Fabrizio Colombo,Irene Sabadini
Publisher : Birkhäuser
Page : 362 pages
File Size : 47,9 Mb
Release : 2016-12-09
Category : Mathematics
ISBN : 9783319425146

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Slice Hyperholomorphic Schur Analysis by Daniel Alpay,Fabrizio Colombo,Irene Sabadini Pdf

This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.

Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress

Michael Ruzhansky,Jens Wirth
Progress In Analysis And Its Applications Proceedings Of The 7th International Isaac Congress Book PDF

Author : Michael Ruzhansky,Jens Wirth
Publisher : World Scientific
Page : 668 pages
File Size : 45,5 Mb
Release : 2010-07-29
Category : Mathematics
ISBN : 9789814464703

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Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress by Michael Ruzhansky,Jens Wirth Pdf

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.

Progress in Analysis and Its Applications

Michael Ruzhansky,Jens Wirth
Progress in Analysis and Its Applications Book PDF

Author : Michael Ruzhansky,Jens Wirth
Publisher : World Scientific
Page : 668 pages
File Size : 48,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814313162

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Progress in Analysis and Its Applications by Michael Ruzhansky,Jens Wirth Pdf

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.