Operator Theory, Systems Theory And

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 theoretical physicists.

Editorial Introduction

vii

J. Ball and V. Vinnikov

Functional Models for Representations of the Cuntz Algebra

1

(60)

T. Banks, T. Constantinescu and J.L. Johnson

Relations on Non-commutative Variables and Associated Orthogonal Polynomials

61

(30)

M. Bessmertnyi

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

91

(16)

S. Eidelman and Y. Krasnov

Operator Methods for Solutions of PDE's Based on Their Symmetries

107

(32)

D.S. Kalyuzhnyi-Verbovetzkii

On the Bessmertnyi Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes

139

(26)

V. Katsnelson and D. Volok

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

165

(40)

M.E. Luna-Elizarrarás and M. Shapiro

Preservation of the Norms of Linear Operators Acting on some Quaternionic Function Spaces

205

(16)

P. Muhly and B. Solel

Hardy Algebras Associated with W-correspondences (Point Evaluation and Schur Class Functions)

221

(22)

M. Putinar

Notes on Generalized Lemniscates

243

(24)

M. Reurings and L. Rodman

One-sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bidisk

267

(34)

F.H. Szafraniec

Favard's Theorem Modulo an Ideal

301

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Operator Theory, Systems Theory And Scattering Theory

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