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Treatise on the Shift Operator

Spectral Function Theory

  • Book
  • © 1986

Overview

Authors:
  1. Nikolaĭ K. Nikol’skiĭ

    1. Leningrad Branch of the Steklov Mathematical Institute, Leningard, USSR

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introductory Lecture. What This Book is About

    • Nikolaĭ K. Nikol’skiĭ
    Pages 1-9

  3. Invariant Subspaces

    • Nikolaĭ K. Nikol’skiĭ
    Pages 10-29

  4. Individual Theorems for the Operator S*

    • Nikolaĭ K. Nikol’skiĭ
    Pages 30-61

  5. Compressions of the Shift and the Spectra of Inner Functions

    • Nikolaĭ K. Nikol’skiĭ
    Pages 62-80

  6. Decomposition into Invariant Subspaces

    • Nikolaĭ K. Nikol’skiĭ
    Pages 81-115

  7. The Triangular Form of the Truncated Shift

    • Nikolaĭ K. Nikol’skiĭ
    Pages 116-130

  8. Bases and Interpolation (Statement of the Problem)

    • Nikolaĭ K. Nikol’skiĭ
    Pages 131-150

  9. Bases and Interpolation (Solution)

    • Nikolaĭ K. Nikol’skiĭ
    Pages 151-176

  10. Operator Interpolation and the Commutant

    • Nikolaĭ K. Nikol’skiĭ
    Pages 177-211

  11. Generalized Spectrality and Interpolation of Germs of Analytic Functions

    • Nikolaĭ K. Nikol’skiĭ
    Pages 212-233

  12. Analysis of the Carleson-Vasyunin Condition

    • Nikolaĭ K. Nikol’skiĭ
    Pages 234-250

  13. On the Line and in the Halfplane

    • Nikolaĭ K. Nikol’skiĭ
    Pages 251-268

  14. Back Matter

    Pages 269-486
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Keywords

About this book

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.

Authors and Affiliations

  • Leningrad Branch of the Steklov Mathematical Institute, Leningard, USSR

    Nikolaĭ K. Nikol’skiĭ

Bibliographic Information

  • Book Title: Treatise on the Shift Operator

  • Book Subtitle: Spectral Function Theory

  • Authors: Nikolaĭ K. Nikol’skiĭ

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-70151-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1986

  • Softcover ISBN: 978-3-642-70153-5Published: 20 November 2011

  • eBook ISBN: 978-3-642-70151-1Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XI, 491

  • Topics: Functional Analysis, Operator Theory

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