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© 1989

Toeplitz Operators and Spectral Function Theory

Essays from the Leningrad Seminar on Operator Theory

  • Editors
  • N. K. Nikolskii
Book

Part of the Operator Theory: Advances and Applications book series (OT, volume 42)

Table of contents

About this book

Introduction

The volume contains selected papers of the Spectral Function Theory seminar, Leningrad Branch of Steklov Mathematical Institute. The papers are mostly devoted to the theory of Toeplitz and model operators. These subjects are considered here from various points of view. Several papers concern the relationships of Toeplitz operators to weighted polynomial approximation. Namely, two papers by B. Solomyak and A. Volberg intensively treat the problem of spectra! multiplicity f~r analytic Toeplitz operators (which are, in fact, multiplication operators) and my paper can serve as an introduction to the problem. This theme of multiplicities is continued in a paper by V. Vasyunin where the multiplicity of the spectrum is computed for Hilbert space contractions with finite defect indices. V. Peller's paper deals with a perturbation theory problem for Toeplitz operators. In a paper by D. Yakubovich a new similarity model for a class of Toeplitz operators is constructed. S. Treil' presents a survey of a part of spectral function theory for vector valued function (Szego-Kolmogorov extreme prob!ems for operator weights, bases of vector rational functions, estimations of Hilbert transform with respect to operator weights, the operator corona problem). As a concluding remark I dare only note that the whole collection convinces us once more without a doubt of the fruitfullness of the natural union of operator theory and complex analysis (if at all the union of these fields is at all different from their intersection).

Keywords

approximation Hilbert space perturbation perturbation theory

Bibliographic information

  • Book Title Toeplitz Operators and Spectral Function Theory
  • Book Subtitle Essays from the Leningrad Seminar on Operator Theory
  • Authors N. Nikolsky
  • Series Title Operator Theory: Advances and Applications
  • DOI https://doi.org/10.1007/978-3-0348-5587-7
  • Copyright Information Birkhäuser Basel 1989
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-2344-8
  • Softcover ISBN 978-3-0348-5589-1
  • eBook ISBN 978-3-0348-5587-7
  • Series ISSN 0255-0156
  • Series E-ISSN 2296-4878
  • Edition Number 1
  • Number of Pages VII, 421
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Science, Humanities and Social Sciences, multidisciplinary
  • Buy this book on publisher's site