Geometric Analysis on Symmetric Spaces: Second EditionAmerican Mathematical Soc., 1989 - 221 pages "This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations - that is, representations on solution spaces of invariant differential equations."--BOOK JACKET. |
Table des matières
| 1 | |
A Duality for Symmetric Spaces | 59 |
The Fourier Transform on a Symmetric Space | 197 |
The Radon Transform on X and on Gsubo Range Questions | 363 |
Differential Equations on Symmetric Spaces | 401 |
Eigenspace Representations | 539 |
Solutions to Exercises | 573 |
| 599 | |
| 627 | |
| 633 | |
Expressions et termes fréquents
analog analytic bijection Cartan Chapter commutative conical distributions conical function consider constant converges convolution Corollary corresponding decomposition deduce defined denote diffeomorphism differential operator dual transform eigenspace representations equation finite-dimensional following result Fourier transform function f G/MN geodesic given Haar measure hand side Harish-Chandra Helgason Hence holomorphic Hom(V horocycle implies integral invariant inversion formula irreducible isomorphism Iwasawa decomposition K-finite K-invariant Killing form Lemma Lie algebra Lie group linear noncompact o e XX orthogonal Paley–Wiener theorem Poisson transform polynomial Prop Proposition prove Radon transform representation of G restricted roots ſ ſ satisfies spherical function spherical transform subgroup subset subspace supp(T surjectivity symmetric space Theorem 1.1 topology transform f vector Weyl chamber Weyl group