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Elements of Functional Analysis

  • Francis Hirsch
  • Gilles Lacombe

Part of the Graduate Texts in Mathematics book series (GTM, volume 192)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Prologue: Sequences

    1. Francis Hirsch, Gilles Lacombe
      Pages 1-24
  3. Function Spaces and Their Duals

    1. Front Matter
      Pages 25-25
    2. Francis Hirsch, Gilles Lacombe
      Pages 27-48
    3. Francis Hirsch, Gilles Lacombe
      Pages 49-95
    4. Francis Hirsch, Gilles Lacombe
      Pages 97-141
    5. Francis Hirsch, Gilles Lacombe
      Pages 143-183
  4. Operators

    1. Front Matter
      Pages 185-185
    2. Francis Hirsch, Gilles Lacombe
      Pages 187-212
    3. Francis Hirsch, Gilles Lacombe
      Pages 213-253
  5. Distributions

    1. Front Matter
      Pages 255-255
    2. Francis Hirsch, Gilles Lacombe
      Pages 257-285
    3. Francis Hirsch, Gilles Lacombe
      Pages 287-316
    4. Francis Hirsch, Gilles Lacombe
      Pages 317-348
    5. Francis Hirsch, Gilles Lacombe
      Pages 349-377
  6. Back Matter
    Pages 379-396

About this book

Introduction

This book arose from a course taught for several years at the Univer­ sity of Evry-Val d'Essonne. It is meant primarily for graduate students in mathematics. To make it into a useful tool, appropriate to their knowl­ edge level, prerequisites have been reduced to a minimum: essentially, basic concepts of topology of metric spaces and in particular of normed spaces (convergence of sequences, continuity, compactness, completeness), of "ab­ stract" integration theory with respect to a measure (especially Lebesgue measure), and of differential calculus in several variables. The book may also help more advanced students and researchers perfect their knowledge of certain topics. The index and the relative independence of the chapters should make this type of usage easy. The important role played by exercises is one of the distinguishing fea­ tures of this work. The exercises are very numerous and written in detail, with hints that should allow the reader to overcome any difficulty. Answers that do not appear in the statements are collected at the end of the volume. There are also many simple application exercises to test the reader's understanding of the text, and exercises containing examples and coun­ terexamples, applications of the main results from the text, or digressions to introduce new concepts and present important applications. Thus the text and the exercises are intimately connected and complement each other.

Keywords

Hilbert space Operator theory calculus convolution differential equation distribution functional analysis

Authors and affiliations

  • Francis Hirsch
    • 1
  • Gilles Lacombe
    • 1
  1. 1.Département de MathématiquesUniversité d’Évry-Val d’EssonneÉvry CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1444-1
  • Copyright Information Springer-Verlag New York, Inc. 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7146-8
  • Online ISBN 978-1-4612-1444-1
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site