Advertisement

Bounded Integral Operators on L2 Spaces

  • Paul Richard Halmos
  • Viakalathur Shankar Sunder
Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 96)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 1-3
  3. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 4-7
  4. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 8-16
  5. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 17-20
  6. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 21-26
  7. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 27-31
  8. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 32-38
  9. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 39-42
  10. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 43-49
  11. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 50-58
  12. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 59-71
  13. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 72-75
  14. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 76-84
  15. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 85-94
  16. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 95-104
  17. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 105-110
  18. Paul Richard Halmos, Viakalathur Shankar Sunder
    Pages 111-118
  19. Back Matter
    Pages 119-134

About this book

Introduction

The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali­ zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea­ sure spaces. The category. Some of the flavor of the theory can be perceived in finite­ dimensional linear algebra. Matrices are sometimes considered to be an un­ natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.

Keywords

Finite Hilbertscher Raum Integral Integraloperator algebra

Authors and affiliations

  • Paul Richard Halmos
    • 1
  • Viakalathur Shankar Sunder
    • 2
  1. 1.Indiana UniversityBloomingtonUSA
  2. 2.University of CaliforniaSanta BarbaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-67016-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1978
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-67018-3
  • Online ISBN 978-3-642-67016-9
  • Buy this book on publisher's site