Groups and geometric analysis : integral geometry, invariant by Sigurdur Helgason PDF

By Sigurdur Helgason

ISBN-10: 0821826735

ISBN-13: 9780821826737

This quantity, the second one of Helgason's awesome 3 books on Lie teams and the geometry and research of symmetric areas, is an creation to group-theoretic tools in research on areas with a bunch motion. the 1st bankruptcy offers with the 3 two-dimensional areas of continuing curvature, requiring purely effortless equipment and no Lie thought. it truly is remarkably available and will be compatible for a first-year graduate path. the rest of the ebook covers extra complex subject matters, together with the paintings of Harish-Chandra and others, yet specially that of Helgason himself. certainly, the exposition will be obvious as an account of the author's great contributions to the topic. bankruptcy I offers with smooth essential geometry and Radon transforms. the second one bankruptcy examines the interconnection among Lie teams and differential operators. bankruptcy IV develops the speculation of round capabilities on semisimple Lie teams with a undeniable measure of completeness, together with a research of Harish-Chandra's $c$-function. The remedy of research on compact symmetric areas (Chapter V) contains a few finite-dimensional illustration conception for compact Lie teams and Fourier research on compact teams. every one bankruptcy ends with routines (with recommendations given on the finish of the book!) and ancient notes. This ebook, that is new to the AMS publishing application, is a superb instance of the author's famous transparent and cautious writing sort. It has turn into the traditional textual content for the research of round services and invariant differential operators on symmetric areas. Sigurdur Helgason was once provided the Steele Prize for teams and Geometric research and the better half quantity, Differential Geometry, Lie teams and Symmetric areas.

Show description

Read or Download Groups and geometric analysis : integral geometry, invariant differential operators, and spherical functions PDF

Similar group theory books

Read e-book online An Account of the Theory of Crystallographic Groups PDF

Court cases of the yank Mathematical Society
Vol. sixteen, No. 6 (Dec. , 1965), pp. 1230-1236
Published via: American Mathematical Society
DOI: 10. 2307/2035904
Stable URL: http://www. jstor. org/stable/2035904
Page count number: 7

Bernard Aupetit's A Primer on Spectral Theory PDF

This textbook presents an creation to the recent thoughts of subharmonic services and analytic multifunctions in spectral concept. issues contain the fundamental result of sensible research, bounded operations on Banach and Hilbert areas, Banach algebras, and functions of spectral subharmonicity.

Download PDF by Jon F. Carlson, L. Townsley, Luís Valero-Elizondo, Mucheng: Cohomology Rings of Finite Groups: With an Appendix:

Crew cohomology has a wealthy heritage that is going again a century or extra. Its origins are rooted in investigations of crew concept and num­ ber concept, and it grew into an indispensable part of algebraic topology. within the final thirty years, staff cohomology has constructed a strong con­ nection with finite team representations.

Extra info for Groups and geometric analysis : integral geometry, invariant differential operators, and spherical functions

Sample text

Proof. Let T e £ ' have the Fourier series (7). Then for each cu b > 0 and each i: > 0, T has a continuous restriction to Ea + r0 and to £ 0 >b + r . 8 [Intro. (z)| z |z|>K M < * < sup \fN(z)\ |z|K By the uniform convergence of fN to 0 on compact sets this implies fN -* 0 in Ea + r 0, as claimed. Consequently, I S e""'0

9sn) denote the Cartesian coordinates of points on S" l. 3. 1. (i) The eigenspaces ofL on S"~l are of the form Ek = span of {famk(s) = (alsi + ••• + ansn)k, seSn~1}. , an)eCn is an isotropic vector and keZ+. The eigenvalue is — k(k + n — 2). (ii) Each eigenspace representation is irreducible. (iii) L2(Sn~l) = YiO Ek (orthogonal Hilbert space decomposition). Proof. Let Pk denote the space of homogeneous polynomial functions p(x 1 ? , x„) of degree k on Rn and Hk cz Pk the subspace of harmonic polynomials.

26). It should be observed that because of (8) the Euclidean and the nonEuclidean harmonic functions coincide. 1. In order to describe the solution to Problem B we need the concept of an analytic functional {hyperfunction) on a compact analytic manifold. Let s/(B) denote the space of analytic functions on the boundary B, considered as an analytic manifold. For each such manifold B, stf(B) carries a certain natural topology; in the case of the circle it can be described rather simply as follows.

Download PDF sample

Groups and geometric analysis : integral geometry, invariant differential operators, and spherical functions by Sigurdur Helgason

by Kevin

Rated 4.61 of 5 – based on 49 votes