Skip to main content
SpringerLink
Log in

Functional Analysis

  • Book
  • © 1995

Overview

Authors:
  1. Kôsaku Yosida

    1. Kamakura, 247, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Classics in Mathematics (CLASSICS)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (15 chapters)

  1. Front Matter

    Pages N1-XII
    Download chapter PDF

  2. Preliminaries

    • Kôsaku Yosida
    Pages 1-22

  3. Semi-norms

    • Kôsaku Yosida
    Pages 23-68

  4. Applications of the Baire-Hausdorff Theorem

    • Kôsaku Yosida
    Pages 68-81

  5. The Orthogonal Projection and F. Riesz’ Representation Theorem

    • Kôsaku Yosida
    Pages 81-101

  6. The Hahn-Banach Theorems

    • Kôsaku Yosida
    Pages 102-119

  7. Strong Convergence and Weak Convergence

    • Kôsaku Yosida
    Pages 119-145

  8. Fourier Transform and Differential Equations

    • Kôsaku Yosida
    Pages 145-193

  9. Dual Operators

    • Kôsaku Yosida
    Pages 193-208

  10. Resolvent and Spectrum

    • Kôsaku Yosida
    Pages 209-231

  11. Analytical Theory of Semi-groups

    • Kôsaku Yosida
    Pages 231-274

  12. Compact Operators

    • Kôsaku Yosida
    Pages 274-293

  13. Normed Rings and Spectral Representation

    • Kôsaku Yosida
    Pages 294-362

  14. Other Representation Theorems in Linear Spaces

    • Kôsaku Yosida
    Pages 362-378

  15. Ergodic Theory and Diffusion Theory

    • Kôsaku Yosida
    Pages 379-418

  16. The Integration of the Equation of Evolution

    • Kôsaku Yosida
    Pages 418-465

  17. Back Matter

    Pages 466-501
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Kamakura, 247, Japan

    Kôsaku Yosida

About the author

Biography of Kôsaku Yosida

Kôsaku Yosida (7.2.1909-20.6.1990) was born in Hiroshima, Japan. After studying mathematics a the University of Tokyo he held posts at Osaka and Nagoya Universities before returning to the University of Tokyo in 1955.

Yosida obtained important and fundamental results in functional analysis and probability. He is best remembered for his joint work with E. Hille which brought forth a theory of semigroups of operators successfully applied to diffusion equations, Markov processes, hyperbolic equations and potential theory. His famous textbook on Functional Analysis was published in 6 distinct editions between 1965 and 1980.

Bibliographic Information

  • Book Title: Functional Analysis

  • Authors: Kôsaku Yosida

  • Series Title: Classics in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-61859-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-58654-8Published: 15 February 1995

  • eBook ISBN: 978-3-642-61859-8Published: 06 December 2012

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 6

  • Number of Pages: XVI, 504

  • Additional Information: Reprint of the 1980 Edition (Grundlehren der mathematischen Wissenschaften, Vol. 123)

  • Topics: Functional Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation