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This self-contained text concentrates on the perspective of analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author describes, in detail, many interesting examples, including formulas 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.Read more
- Self-contained and elementary presentation of Lie group theory, concentrating on analysis on Lie groups
- Numerous applications to classical harmonic analysis, useful for the study of the theory of random matrices
- Many exercises and worked examples mean this is ideal for a graduate course on analysis on Lie groups
Reviews & endorsements
"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
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- Date Published: June 2008
- format: Hardback
- isbn: 9780521719308
- length: 314 pages
- dimensions: 235 x 155 x 20 mm
- weight: 0.55kg
- contains: 6 b/w illus. 95 exercises
- availability: Available
Table of Contents
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
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