Schur Functions Operator Colligations And Reproducing Kernel Pontryagin Spaces PDF Download
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| 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 | : 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 | : Birkhäuser |
| Total Pages | : 362 |
| Release | : 2016-12-09 |
| Genre | : Mathematics |
| ISBN | : 3319425145 |
Download Slice Hyperholomorphic Schur Analysis Book in PDF, ePub and Kindle
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.
| Author | : Daniel Alpay |
| Publisher | : Birkhäuser |
| Total Pages | : 495 |
| Release | : 2018-01-30 |
| Genre | : Mathematics |
| ISBN | : 3319688499 |
Download Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations Book in PDF, ePub and Kindle
This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer’s chief research interests and will appeal to a broad readership whose work involves operator theory.
| Author | : Sheldon Jay Axler |
| Publisher | : Cambridge University Press |
| Total Pages | : 490 |
| Release | : 1998-05-28 |
| Genre | : Mathematics |
| ISBN | : 9780521631938 |
Download Holomorphic Spaces Book in PDF, ePub and Kindle
Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.
| Author | : Marinus A. Kaashoek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 478 |
| Release | : 2006-01-17 |
| Genre | : Mathematics |
| ISBN | : 3764373989 |
Download Recent Advances in Operator Theory and Its Applications Book in PDF, ePub and Kindle
This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.
| Author | : Daniel Alpay |
| Publisher | : Birkhäuser |
| Total Pages | : 521 |
| Release | : 2015-11-13 |
| Genre | : Mathematics |
| ISBN | : 3319160591 |
Download An Advanced Complex Analysis Problem Book Book in PDF, ePub and Kindle
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.
| 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.
| Author | : Alexander A. Borichev |
| Publisher | : Birkhäuser |
| Total Pages | : 536 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3034883625 |
Download Systems, Approximation, Singular Integral Operators, and Related Topics Book in PDF, ePub and Kindle
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.
| Author | : Emmanuel Fricain |
| Publisher | : Cambridge University Press |
| Total Pages | : 703 |
| Release | : 2016-05-26 |
| Genre | : Mathematics |
| ISBN | : 1316060918 |
Download The Theory of H(b) Spaces: Volume 1 Book in PDF, ePub and Kindle
An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
