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Universitext

Analysis IV

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

Authors: Godement, Roger

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  • Prefers ideas to calculations
  • Explains the ideas without parsimony of words
  • Based on 35 years of teaching at Paris University
  • Blends mathematics skillfully with didactical and historical considerations
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eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-319-16907-1
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  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-319-16906-4
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  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

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.

Reviews

“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)


Table of contents (17 chapters)

Table of contents (17 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-319-16907-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-319-16906-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Analysis IV
Book Subtitle
Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights
Authors
Translated by
Ray, U.
Series Title
Universitext
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-16907-1
DOI
10.1007/978-3-319-16907-1
Softcover ISBN
978-3-319-16906-4
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XI, 527
Number of Illustrations
4 b/w illustrations
Topics