Analysis on Lie Groups
Analysis on Lie Groups
£80.99
GBPThe 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.
- 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
Product details
May 2008Hardback
9780521719308
314 pages
235 × 155 × 20 mm
0.55kg
6 b/w illus. 95 exercises
Available
Table of Contents
- 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.
