Analysis IV

Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights

  • Roger Godement

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. XI – Integration and Fourier Transform

    1. Front Matter
      Pages 1-4
    2. Roger Godement
      Pages 5-19
    3. Roger Godement
      Pages 20-36
    4. Roger Godement
      Pages 37-52
    5. Roger Godement
      Pages 53-102
    6. Roger Godement
      Pages 103-117
    7. Roger Godement
      Pages 118-172
    8. Roger Godement
      Pages 173-203
  3. XII –The Garden of Modular Delights or The Opium of Mathematicians

    1. Front Matter
      Pages 261-261
    2. Roger Godement
      Pages 261-280
    3. Roger Godement
      Pages 298-315
    4. Roger Godement
      Pages 316-348
    5. Roger Godement
      Pages 349-375
    6. Roger Godement
      Pages 376-393
    7. Roger Godement
      Pages 394-440
    8. Roger Godement
      Pages 441-462
    9. Roger Godement
      Pages 463-509
  4. Back Matter
    Pages 511-527

About this book


Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be modern and classical, is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.


compact level spaces elliptic functions integrable functions modular functions spaces spectral theory zeta functions

Authors and affiliations

  • Roger Godement
    • 1
  1. 1.ParisFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16906-4
  • Online ISBN 978-3-319-16907-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site