Spectral Theory of Operators in Hilbert Space

  • K. O. Friedrichs

Part of the Applied Mathematical Sciences book series (AMS, volume 9)

Table of contents

  1. Front Matter
    Pages N1-ix
  2. K. O. Friedrichs
    Pages 1-30
  3. K. O. Friedrichs
    Pages 31-63
  4. K. O. Friedrichs
    Pages 64-94
  5. K. O. Friedrichs
    Pages 95-142
  6. K. O. Friedrichs
    Pages 143-162
  7. K. O. Friedrichs
    Pages 163-185
  8. K. O. Friedrichs
    Pages 186-212
  9. K. O. Friedrichs
    Pages 213-240
  10. Back Matter
    Pages 241-245

About this book

Introduction

The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica­ tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.

Keywords

Hilbert space Operators calculus equation function theorem

Authors and affiliations

  • K. O. Friedrichs
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-6396-8
  • Copyright Information Springer-Verlag New York 1973
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90076-6
  • Online ISBN 978-1-4612-6396-8
  • Series Print ISSN 0066-5452
  • About this book
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