© 2015

Analysis IV

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


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

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

  1. 1.ParisFrance

About the authors

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Bibliographic information

  • Book Title Analysis IV
  • Book Subtitle Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights
  • Authors Roger Godement
  • Series Title Universitext
  • Series Abbreviated Title Universitext
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-16906-4
  • eBook ISBN 978-3-319-16907-1
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages XI, 527
  • Number of Illustrations 4 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
  • Buy this book on publisher's site


“The author includes many interesting historical comments of great value for those interested in the history of mathematics. The author includes sometimes examples and exercises which help the reader to understand the theory presented.” (Dumitrŭ Popa, zbMATH 1331.28001, 2016)