Record:   Prev Next
Author Faraut, Jacques
Title Analysis on Lie Groups : An Introduction
Imprint Cambridge : Cambridge University Press, 2008
©2008
book jacket
Descript 1 online resource (314 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Cambridge Studies in Advanced Mathematics ; v.110
Cambridge Studies in Advanced Mathematics
Note Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- 1 The linear group -- 1.1 Topological groups -- 1.2 The group GL(n,R) -- 1.3 Examples of subgroups of GL(n,R) -- 1.4 Polar decomposition in GL(n,R) -- 1.5 The orthogonal group -- 1.6 Gram decomposition -- 1.7 Exercises -- 2 The exponential map -- 2.1 Exponential of a matrix -- 2.2 Logarithm of a matrix -- 2.3 Exercises -- 3 Linear Lie groups -- 3.1 One parameter subgroups -- 3.2 Lie algebra of a linear Lie group -- 3.3 Linear Lie groups are submanifolds -- 3.4 Campbell-Hausdorff formula -- 3.5 Exercises -- 4 Lie algebras -- 4.1 Definitions and examples -- 4.2 Nilpotent and solvable Lie algebras -- 4.3 Semi-simple Lie algebras -- 4.4 Exercises -- 5 Haar measure -- 5.1 Haar measure -- 5.2 Case of a group which is an open set in Rn -- 5.3 Haar measure on a product -- 5.4 Some facts about differential calculus -- 5.5 Invariant vector fields and the Haar measure on a linear Lie group -- 5.6 Exercises -- 6 Representations of compact groups -- 6.1 Unitary representations -- 6.2 Compact self-adjoint operators -- 6.3 Schur orthogonality relations -- 6.4 Peter-Weyl Theorem -- 6.5 Characters and central functions -- 6.6 Absolute convergence of Fourier series -- 6.7 Casimir operator -- 6.8 Exercises -- 7 The groups SU(2) and SO(3), Haar measures, and irreducible representations -- 7.1 Adjoint representation of SU(2) -- 7.2 Haar measure on SU(2) -- 7.3 The group SO(3) -- 7.4 Euler angles -- 7.5 Irreducible representations of SU(2) -- 7.6 Irreducible representations of SO(3) -- 7.7 Exercises -- 8 Analysis on the group SU(2) -- 8.1 Fourier series on SO(2) -- 8.2 Functions of class Ck -- 8.3 Laplace operator on the group SU(2) -- 8.4 Uniform convergence of Fourier series on the group SU(2) -- 8.5 Heat equation on SO(2) -- 8.6 Heat equation on SU(2) -- 8.7 Exercises
9 Analysis on the sphere and the Euclidean space -- 9.1 Integration formulae -- 9.2 Laplace operator -- 9.3 Spherical harmonics -- 9.4 Spherical polynomials -- 9.5 Funk-Hecke Theorem -- 9.6 Fourier transform and Bochner-Hecke relations -- 9.7 Dirichlet problem and Poisson kernel -- 9.8 An integral transform -- 9.9 Heat equation -- 9.10 Exercises -- 10 Analysis on the spaces of symmetric and Hermitian matrices -- 10.1 Integration formulae -- 10.2 Radial part of the Laplace operator -- 10.3 Heat equation and orbital integrals -- 10.4 Fourier transforms of invariant functions -- 10.5 Exercises -- 11 Irreducible representations of the unitary group -- 11.1 Highest weight theorem -- 11.2 Weyl formulae -- 11.3 Holomorphic representations -- 11.4 Polynomial representations -- 11.5 Exercises -- 12 Analysis on the unitary group -- 12.1 Laplace operator -- 12.2 Uniform convergence of Fourier series on the unitary group -- 12.3 Series expansions of central functions -- 12.4 Generalised Taylor series -- 12.5 Radial part of the Laplace operator on the unitary group -- 12.6 Heat equation on the unitary group -- 12.7 Exercises -- Bibliography -- Index
A self-contained and elementary presentation of Lie group theory, with numerous exercises and worked examples ideal for a graduate course
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Faraut, Jacques Analysis on Lie Groups : An Introduction Cambridge : Cambridge University Press,c2008 9780521719308
Subject Lie groups
Electronic books
Record:   Prev Next