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Treatise on the Shift Operator

Spectral Function Theory

  • Nikolaĭ K. Nikol’skiĭ

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 273)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Nikolaĭ K. Nikol’skiĭ
    Pages 1-9
  3. Nikolaĭ K. Nikol’skiĭ
    Pages 10-29
  4. Nikolaĭ K. Nikol’skiĭ
    Pages 30-61
  5. Nikolaĭ K. Nikol’skiĭ
    Pages 62-80
  6. Nikolaĭ K. Nikol’skiĭ
    Pages 81-115
  7. Nikolaĭ K. Nikol’skiĭ
    Pages 116-130
  8. Nikolaĭ K. Nikol’skiĭ
    Pages 131-150
  9. Nikolaĭ K. Nikol’skiĭ
    Pages 151-176
  10. Nikolaĭ K. Nikol’skiĭ
    Pages 177-211
  11. Nikolaĭ K. Nikol’skiĭ
    Pages 234-250
  12. Nikolaĭ K. Nikol’skiĭ
    Pages 251-268
  13. Back Matter
    Pages 269-486

About this book

Introduction

This book is an elementary introduction to non-classical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one­ dimensional rank of non-unitarity (rank(I - T*T) = rank(I - TT*) = 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself. The functional model of Sz. -Nagy and Foia§ re­ duces the study of general operators to an investigation of the . compression T=PSIK of the shift operator S, Sf = zf, onto coinvariant subspaces (i. e. subspaces in­ variant with respect to the adjoint shift S*). In the main body of the book (the "Lectures" in the proper meaning of the word) this operator acts on the Hardy space H2 and is itself a part of the operator of multiplication by the independent variable in the space L2 (in the case at hand L2 means L2(lf), If being the unit circle), this operator again being fundamental for classical spectral theory.

Keywords

Hardy space Invariant Multiplication Operators Schaltoperator analytic function class development form function functional model operator spectral theory variable

Authors and affiliations

  • Nikolaĭ K. Nikol’skiĭ
    • 1
  1. 1.Leningrad Branch of the Steklov Mathematical InstituteLeningardUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-70151-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1986
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-70153-5
  • Online ISBN 978-3-642-70151-1
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site