Analysis IV

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

Roger Godement (Autor)

Buch | Softcover

XI, 527 Seiten

2015 | 2015
Springer International Publishing (Verlag)
978-3-319-16906-4 (ISBN)

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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.

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.

XI Integration and Fourier Transform.- XII The Garden of Modular Delights or The Opium of Mathematicians.

"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." (Dumitr Popa, zbMATH 1331.28001, 2016)

Erscheint lt. Verlag	13.5.2015
Reihe/Serie	Universitext
Übersetzer	Urmie Ray
Zusatzinfo	XI, 527 p. 4 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	829 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	compact level spaces • elliptic functions • integrable functions • modular functions • Spaces • spectral theory • Zeta functions
ISBN-10	3-319-16906-8 / 3319169068
ISBN-13	978-3-319-16906-4 / 9783319169064
Zustand	Neuware