System Theory, the Schur Algorithm and Multidimensional Analysis
System Theory, the Schur Algorithm and Multidimensional Analysis

Author: Daniel Alpay

Publisher: Springer Science & Business Media

Published: 2007-03-20

Total Pages: 331

ISBN-13: 3764381361

DOWNLOAD EBOOK

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.

System Theory, the Schur Algorithm and Multidimensional Analysis
System Theory, the Schur Algorithm and Multidimensional Analysis

Author: Daniel Alpay

Publisher: Springer Science & Business Media

Published: 2007-06-28

Total Pages: 331

ISBN-13: 376438137X

DOWNLOAD EBOOK

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.

System Theory, the Schur Algorithm and Multidimensional Analysis
System Theory, the Schur Algorithm and Multidimensional Analysis

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2009-09-03

Total Pages: 322

ISBN-13: 9783764391874

DOWNLOAD EBOOK

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.

Slice Hyperholomorphic Schur Analysis
Slice Hyperholomorphic Schur Analysis

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2016-12-09

Total Pages: 365

ISBN-13: 3319425145

DOWNLOAD EBOOK

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.

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations
Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2018-01-30

Total Pages: 501

ISBN-13: 3319688499

DOWNLOAD EBOOK

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.

An Advanced Complex Analysis Problem Book
An Advanced Complex Analysis Problem Book

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2015-11-13

Total Pages: 523

ISBN-13: 3319160591

DOWNLOAD EBOOK

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.

Advances in Complex Analysis and Operator Theory
Advances in Complex Analysis and Operator Theory

Author: Fabrizio Colombo

Publisher: Birkhäuser

Published: 2017-09-30

Total Pages: 398

ISBN-13: 3319623621

DOWNLOAD EBOOK

This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

Advancements in Complex Analysis
Advancements in Complex Analysis

Author: Daniel Breaz

Publisher: Springer Nature

Published: 2020-05-12

Total Pages: 538

ISBN-13: 3030401200

DOWNLOAD EBOOK

The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.

Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications

Author: Michele Benzi

Publisher: Springer

Published: 2017-01-24

Total Pages: 413

ISBN-13: 3319498878

DOWNLOAD EBOOK

Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.

Interpolation, Schur Functions and Moment Problems II
Interpolation, Schur Functions and Moment Problems II

Author: Daniel Alpay

Publisher: Springer Science & Business Media

Published: 2012-07-25

Total Pages: 306

ISBN-13: 3034804288

DOWNLOAD EBOOK

The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.​