Author: Daniel Alpay
Publisher: Birkhäuser Basel
Keywords: applications, theory, advances, operator, reproducing, spaces, kernel
Number of Pages: 344
Published: 2003-12-11
List price: $149.00
ISBN-10: 376430068X
ISBN-13: 9783764300685

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

Authors:Daniel Alpay, Victor Vinnikov,
Publisher: Birkhäuser Basel
Keywords: theory, operator, volume, applications, anniversary, advances, moshe, system, related, topics, livsic
Number of Pages: 567
Published: 2001-04-20
List price: unknow
ISBN-10: 3764365234
ISBN-13: 9783764365233

The present selection of refereed papers is dedicated to Moshe Livic on the occasion of his eightieth anniversary. It covers many areas of operator theory and its applications, reflecting the breadth and the profound impact of his work. In particular, some of his most recent ideas on 2D-systems are presented. Other contributions cover important avenues of modern operator theory in such fields as interpolation theory (also in the so-called nonstationary setting), direct and inverse problems for the string equation and for nonselfadjoint differential operators, operator models and function theor

Author: Daniel Alpay; Israel Gohberg
Publisher: Birkhauser
Keywords: linear, applications, advances, operators, systems, theory, operator, space, method, generalizations, state
Number of Pages: 270
Published: 2005-12-07
List price: $169.00
ISBN-10: 3764373709
ISBN-13: 9783764373702

The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations.

Authors:Daniel Alpay, Victor Vinnikov,
Publisher: Birkhäuser Basel
Keywords: theory, operator, advances, applications, analysis, multidimensional, schur, algorithm, system
Number of Pages: 322
Published: 2007-04-19
List price: $189.00
ISBN-10: 3764381361
ISBN-13: 9783764381363

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 during the period June 26-July 1, 2005. The papers present the newest developments in key directions of current research in complex analysis and operator theory. Topics considered include Schur analysis, hierarchical semiseparable matrices, canonical forms for pairs of quaternionic matrices, the theory of homogeneous operat

Authors:Daniel Alpay, Israel Gohberg,
Publisher: Birkhäuser Basel
Keywords: linear, applications, advances, operators, systems, theory, operator, schur, functions, moment, problems, interpolation
Number of Pages: 302
Published: 2006-04-28
List price: $189.00
ISBN-10: 3764375469
ISBN-13: 9783764375461

Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others. This volume is almost

Authors:Daniel Alpay, Victor Vinnikov,
Publisher: Birkhäuser Basel
Keywords: theory, operator, advances, applications, generalizations, scattering, systems, multidimensional
Number of Pages: 310
Published: 2005-05-31
List price: $169.00
ISBN-10: 3764372125
ISBN-13: 9783764372125

Operator theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves the setting of one operator and considers several operators, the situation is much more involved. There is no longer a single underlying theory, but rather different theories, some of them loosely connected and some not connected at all. These various theories, which one could call "multidimensional operator theory", are topics of active and intensive research.The present volu

Authors:Daniel Alpay, Victor Vinnikov,
Publisher: Birkhäuser Basel
Keywords: functions, operator, theory, applications, volume, advances, livsic, scattering, transfer, moshe, characteristic, memorial
Number of Pages: 408
Published: 2009-12-28
List price: $179.00
ISBN-10: 3034601824
ISBN-13: 9783034601825

The notions of transfer function and characteristic functions proved to be fundamental in the last fifty years in operator theory and in system theory. Moshe Livsic played a central role in developing these notions, and the book contains a selection of carefully chosen refereed papers dedicated to his memory. Topics include classical operator theory, ergodic theory and stochastic processes, geometry of smooth mappings, mathematical physics, Schur analysis and system theory. The variety of topics attests well to the breadth of Moshe Livsic’s mathematical vision and the deep impact of his