By Sigurdur Helgason
This quantity, the second one of Helgason's extraordinary 3 books on Lie teams and the geometry and research of symmetric areas, is an advent to group-theoretic equipment in research on areas with a bunch motion. the 1st bankruptcy bargains with the 3 two-dimensional areas of continuing curvature, requiring in simple terms easy tools and no Lie concept. it really is remarkably obtainable and will be compatible for a first-year graduate direction. the rest of the booklet covers extra complex subject matters, together with the paintings of Harish-Chandra and others, yet in particular that of Helgason himself. certainly, the exposition will be noticeable as an account of the author's large contributions to the topic. bankruptcy I bargains with sleek imperative geometry and Radon transforms. the second one bankruptcy examines the interconnection among Lie teams and differential operators. bankruptcy IV develops the speculation of round services on semisimple Lie teams with a definite measure of completeness, together with a learn of Harish-Chandra's $c$-function. The therapy of study on compact symmetric areas (Chapter V) contains a few finite-dimensional illustration concept for compact Lie teams and Fourier research on compact teams. each one bankruptcy ends with routines (with ideas given on the finish of the book!) and ancient notes. This booklet, that's new to the AMS publishing application, is a superb instance of the author's famous transparent and cautious writing kind. It has turn into the traditional textual content for the learn of round capabilities and invariant differential operators on symmetric areas. Sigurdur Helgason was once offered the Steele Prize for teams and Geometric research and the significant other quantity, Differential Geometry, Lie teams and Symmetric areas.
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