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Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations

  • Book
  • © 2005

Overview

Editors:
  1. Daniel Alpay

    1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

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  2. Victor Vinnikov

    1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

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    You can also search for this editor in PubMed   Google Scholar

  • Focussed selection of invited contributions of experts in the area
  • Establishing 'multidimensional operator theory' as a working field

Part of the book series: Operator Theory: Advances and Applications (OT, volume 157)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Functional Models for Representations of the Cuntz Algebra

    • Joseph A. Ball, Victor Vinnikov
    Pages 1-60

  3. Relations on Non-commutative Variables and Associated Orthogonal Polynomials

    • T. Banks, T. Constantinescu, J.L. Johnson
    Pages 61-90

  4. Functions of Several Variables in the Theory of Finite Linear Structures Part I: Analysis

    • M. Bessmertnyĭ
    Pages 91-106

  5. Operator Method for Solution of PDEs Based on Their Symmetries

    • Samuil D. Eidelman, Yakov Krasnov
    Pages 107-137

  6. On the Bessmertnyĭ Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes

    • Dmitry S. Kalyuzhnyĭ-Verbovetzkiĭ
    Pages 139-164

  7. Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions II

    • Victor Katsnelson, Dan Volok
    Pages 165-203

  8. Preservation of the Norms of Linear Operators Acting on Some Quaternionic Function Spaces

    • M. Elena Luna-Elizarrarás, Michael Shapiro
    Pages 205-220

  9. Hardy Algebras Associated with W*-Correspondences (Point Evaluation and Schur Class Functions)

    • Paul S. Muhly, Baruch Solel
    Pages 221-241

  10. Notes on Generalized Lemniscates

    • Mihai Putinar
    Pages 243-266

  11. One-Sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bidisk

    • M.C.B. Reurings, L. Rodman
    Pages 267-300

  12. Favard’s Theorem Modulo an Ideal

    • Franciszek Hugon Szafraniec
    Pages 301-310
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Keywords

About this book

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 volume contains a selection of papers in multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations.
The volume will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoreticalphysicists.

Editors and Affiliations

  • Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Daniel Alpay, Victor Vinnikov

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