Functional Analysis

  • Kôsaku Yosida

Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Kôsaku Yosida
    Pages 1-22
  3. Kôsaku Yosida
    Pages 23-68
  4. Kôsaku Yosida
    Pages 68-81
  5. Kôsaku Yosida
    Pages 102-119
  6. Kôsaku Yosida
    Pages 119-145
  7. Kôsaku Yosida
    Pages 145-193
  8. Kôsaku Yosida
    Pages 193-208
  9. Kôsaku Yosida
    Pages 209-231
  10. Kôsaku Yosida
    Pages 231-274
  11. Kôsaku Yosida
    Pages 274-293
  12. Kôsaku Yosida
    Pages 294-362
  13. Kôsaku Yosida
    Pages 362-378
  14. Kôsaku Yosida
    Pages 379-418
  15. Kôsaku Yosida
    Pages 418-445
  16. Back Matter
    Pages 447-476

About this book

Introduction

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo­ logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe­ maticians, both pure and applied. The reader may pass, e. g. , from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

Keywords

Analysis Hilbert space calculus differential equation functional analysis

Authors and affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Research Institute for Mathematical SciencesUniversity of KyotoKyotoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-00781-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1971
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-00783-9
  • Online ISBN 978-3-662-00781-5
  • Series Print ISSN 0072-7830
  • About this book
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