Analysis on Lie Groups
An Introduction
Published on 22. May 2008
Book
Hardback
314 pages
978-0-521-71930-8 (ISBN)
Description
The subject of analysis on Lie groups comprises an eclectic group of topics which can be treated from many different perspectives. This self-contained text concentrates on the perspective of analysis, to the topics and methods of non-commutative harmonic analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author avoids unessential technical discussions and instead describes in detail many interesting examples, including formulae which have not previously appeared in book form. Topics covered include the Haar measure and invariant integration, spherical harmonics, Fourier analysis and the heat equation, Poisson kernel, the Laplace equation and harmonic functions. Perfect for advanced undergraduates and graduates in geometric analysis, harmonic analysis and representation theory, the tools developed will also be useful for specialists in stochastic calculation and the statisticians. With numerous exercises and worked examples, the text is ideal for a graduate course on analysis on Lie groups.
Reviews / Votes
"The main themes are carefully explained and illustrated by well-chosen examples. He succeeds in putting a remarkable wealth of material into a 300-page book which will certainly serve as a basis for many courses on the subject."Joachim Hilgert, Mathematical Reviews
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises; 6 Line drawings, unspecified
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 23 mm
Weight
662 gr
ISBN-13
978-0-521-71930-8 (9780521719308)
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Schweitzer Classification
Other editions
Additional editions
E-Book
09/2008
1st Edition
Cambridge University Press
€79.99
Available for download
Person
Jacques Faraut is Professeur Emerite in the Institut de Mathematiques de Jussieu at the Universite Pierre et Marie Curie in Paris.
Content
Preface; 1. The linear group; 2. The exponential map; 3. Linear Lie groups; 4. Lie algebras; 5. Haar measure; 6. Representations of compact groups; 7. The groups SU(2) and SO(3), Haar measure; 8. Analysis on the group SU(2); 9. Analysis on the sphere; 10. Analysis on the spaces of symmetric and Hermitian matrices; 11. Irreducible representations of the unitary group; 12. Analysis on the unitary group; Bibliography; Index.