01690 - Analysis on Lie Groups - An Introduction [Faraut].pdf

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Analysis on Lie Groups
An Introduction
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 non-essential technical discussion 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, the 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 statistics. With numerous exercises and worked
examples, the text is ideal for a graduate course on analysis on Lie groups.
Jacques Faraut
is Professeur em´ rite in the Institut de Math´ matiques de Jussieu
´ e
e
at the Universit´ Pierre et Marie Curie in Paris.
e
CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS
Editorial Board:
B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak, B. Simon, B. Totaro
All the titles listed below can be obtained from good booksellers or from Cambridge University
Press. For a complete series listing visit: http://www.cambridge.org/series/sSeries.asp?code=CSAM
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M. P. Brodmann & R. Y. Sharp
Local Cohomology
J. D. Dixon
et al. Analytic pro-p Groups
R. Stanley
Enumerative Combinatorics II
R. M. Dudley
Uniform Central Limit Theorems
J. Jost & X. Li-Jost
Calculus of Variations
A. J. Berrick & M. E. Keating
An Introduction to Rings and Modules
S. Morosawa
Holomorphic Dynamics
A. J. Berrick & M. E. Keating
Categories and Modules with K-theory in View
K. Sato
Levy Processes and Infinitely Divisible Distributions
H. Hida
Modular Forms and Galois Cohomology
R. Iorio & V. Iorio
Fourier Analysis and Partial Differential Equations
R. Blei
Analysis in Integer and Fractional Dimensions
F. Borceaux & G. Janelidze
Galois Theories
B. Bollob´ s
Random Graphs
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R. M. Dudley
Real Analysis and Probability
T. Sheil-Small
Complex Polynomials
C. Voisin
Hodge Theory and Complex Algebraic Geometry, I
C. Voisin
Hodge Theory and Complex Algebraic Geometry, II
V. Paulsen
Completely Bounded Maps and Operator Algebras
F. Gesztesy & H. Holden
Soliton Equations and Their Algebro-Geometric Solutions, I
S. Mukai
An Introduction to Invariants and Moduli
G. Tourlakis
Lectures in Logic and Set Theory, I
G. Tourlakis
Lectures in Logic and Set Theory, II
R. A. Bailey
Association Schemes
J. Carlson, S. M¨ ller-Stach & C. Peters
Period Mappings and Period Domains
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J. J. Duistermaat & J. A. C. Kolk
Multidimensional Real Analysis, I
J. J. Duistermaat & J. A. C. Kolk
Multidimensional Real Analysis, II
M. Golumbic & A. Trenk
Tolerance Graphs
L. Harper
Global Methods for Combinatorial Isoperimetric Problems
I. Moerdijk & J. Mrcun
Introduction to Foliations and Lie Groupoids
J. Kollar, K. E. Smith & A. Corti
Rational and Nearly Rational Varieties
D. Applebaum
Levy Processes and Stochastic Calculus
B. Conrad
Modular Forms and the Ramanujan Conjecture
M. Schechter
An Introduction to Nonlinear Analysis
R. Carter
Lie Algebras of Finite and Affine Type
H. L. Montgomery, R. C Vaughan & M. Schechter
Multiplicative Number Theory, I
I. Chavel
Riemannian Geometry
D. Goldfeld
Automorphic Forms and L-Functions for the Group GL(n,R)
M. Marcus & J. Rosen
Markov Processes, Gaussian Processes, and Local Times
P. Gille & T. Szamuely
Central Simple Algebras and Galois Cohomology
J. Bertoin
Random Fragmentation and Coagulation Processes
E. Frenkel
Langlands Correspondence for Loop Groups
A. Ambrosetti & A. Malchiodi
Nonlinear Analysis and Semilinear Elliptic Problems
T. Tao & V. H. Vu
Additive Combinatorics
E. B. Davies
Linear Operators and their Spectra
K. Kodaira
Complex Analysis
T. Ceccherini-Silberstein, F. Scarabotti, F. Tolli
Harmonic Analysis on Finite Groups
H. Geiges
An Introduction to Contact Topology
Analysis on Lie Groups
An Introduction
JACQUES FARAUT

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