The Schur Algorithm Reproducing Kernel Spaces And System Theory PDF Download
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Author | : Daniel Alpay |
Publisher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 2001 |
Genre | : Computers |
ISBN | : 9780821821558 |
Download The Schur Algorithm, Reproducing Kernel Spaces and System Theory Book in PDF, ePub and Kindle
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.
Author | : Daniel Alpay |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2007-06-28 |
Genre | : Mathematics |
ISBN | : 376438137X |
Download System Theory, the Schur Algorithm and Multidimensional Analysis Book in PDF, ePub and Kindle
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.
Author | : Daniel Alpay |
Publisher | : Birkhäuser |
Total Pages | : 355 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880774 |
Download Reproducing Kernel Spaces and Applications Book in PDF, ePub and Kindle
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.
Author | : Daniel Alpay |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2007-03-20 |
Genre | : Mathematics |
ISBN | : 3764381361 |
Download System Theory, the Schur Algorithm and Multidimensional Analysis Book in PDF, ePub and Kindle
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.
Author | : Saburou Saitoh |
Publisher | : Springer |
Total Pages | : 464 |
Release | : 2016-10-14 |
Genre | : Mathematics |
ISBN | : 9811005303 |
Download Theory of Reproducing Kernels and Applications Book in PDF, ePub and Kindle
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.
Author | : Travis D Andrews |
Publisher | : Springer Science & Business Media |
Total Pages | : 461 |
Release | : 2013-01-04 |
Genre | : Mathematics |
ISBN | : 0817683798 |
Download Excursions in Harmonic Analysis, Volume 2 Book in PDF, ePub and Kindle
The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts: Volume I · Sampling Theory · Remote Sensing · Mathematics of Data Processing · Applications of Data Processing Volume II · Measure Theory · Filtering · Operator Theory · Biomathematics Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government. Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Author | : Joseph A. Ball |
Publisher | : Springer Science & Business Media |
Total Pages | : 340 |
Release | : 2007-12-22 |
Genre | : Mathematics |
ISBN | : 3764385391 |
Download Recent Advances in Matrix and Operator Theory Book in PDF, ePub and Kindle
This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005.
Author | : Daniel Alpay |
Publisher | : Birkhäuser |
Total Pages | : 244 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034889089 |
Download Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces Book in PDF, ePub and Kindle
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.
Author | : Daniel Alpay |
Publisher | : Springer Science & Business Media |
Total Pages | : 107 |
Release | : 2014-03-19 |
Genre | : Mathematics |
ISBN | : 3319051105 |
Download Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis Book in PDF, ePub and Kindle
This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.
Author | : Daniel Alpay |
Publisher | : Birkhäuser |
Total Pages | : 420 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034882157 |
Download Interpolation Theory, Systems Theory and Related Topics Book in PDF, ePub and Kindle
This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.