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Integrals and Operators

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  • © 1978
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Authors:
  1. Irving E. Segal

    1. Massachusetts Institute of Technology, Cambridge, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Ray A. Kunze

    1. University of California at Irvine, Irvine, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 228)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    • Irving E. Segal, Ray A. Kunze
    Pages 1-17
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  3. Basic Integrals

    • Irving E. Segal, Ray A. Kunze
    Pages 18-42
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  4. Measurable Functions and Their Integrals

    • Irving E. Segal, Ray A. Kunze
    Pages 43-92
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  5. Convergence and Differentiation

    • Irving E. Segal, Ray A. Kunze
    Pages 93-122
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  6. Locally Compact and Euclidean Spaces

    • Irving E. Segal, Ray A. Kunze
    Pages 123-151
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  7. Function Spaces

    • Irving E. Segal, Ray A. Kunze
    Pages 152-174
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  8. Invariant Integrals

    • Irving E. Segal, Ray A. Kunze
    Pages 175-205
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  9. Algebraic Integration Theory

    • Irving E. Segal, Ray A. Kunze
    Pages 206-238
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  10. Spectral Analysis in Hilbert Space

    • Irving E. Segal, Ray A. Kunze
    Pages 239-257
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  11. Group Representations and Unbounded Operators

    • Irving E. Segal, Ray A. Kunze
    Pages 258-302
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  12. Semigroups and Perturbation Theory

    • Irving E. Segal, Ray A. Kunze
    Pages 303-323
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  13. Operator Rings and Spectral Multiplicity

    • Irving E. Segal, Ray A. Kunze
    Pages 324-339
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  14. C*-Algebras and Applications

    • Irving E. Segal, Ray A. Kunze
    Pages 340-350
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  15. The Trace as a Non-Commutative Integral

    • Irving E. Segal, Ray A. Kunze
    Pages 351-364
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  16. Back Matter

    Pages 365-374
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Keywords

About this book

TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in har­ monic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elements of the gram­ mar of analysis, of use in group representation theory and elsewhere. The v vi Preface to the Second Edition theory of the trace for operators on Hilbert space is both important in itself and a natural extension of earlier integration-theoretic ideas.

Authors and Affiliations

  • Massachusetts Institute of Technology, Cambridge, USA

    Irving E. Segal

  • University of California at Irvine, Irvine, USA

    Ray A. Kunze

Bibliographic Information

  • Book Title: Integrals and Operators

  • Authors: Irving E. Segal, Ray A. Kunze

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-66693-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1978

  • Softcover ISBN: 978-3-642-66695-7Published: 18 October 2011

  • eBook ISBN: 978-3-642-66693-3Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 2

  • Number of Pages: XIV, 374

  • Additional Information: Originally published by McGraw Hill

  • Topics: Analysis

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