By Sigurdur Helgason
This booklet provides the 1st systematic exposition of geometric research on Riemannian symmetric areas and its courting to the illustration conception of Lie teams. The e-book starts off with smooth indispensable geometry for double fibrations and treats a number of examples intimately. After discussing the speculation of Radon transforms and Fourier transforms on symmetric areas, inversion formulation, and variety theorems, Helgason examines purposes to invariant differential equations on symmetric areas, lifestyles theorems, and specific resolution formulation, relatively capability concept and wave equations. The canonical multitemporal wave equation on a symmetric area is integrated. The booklet concludes with a bankruptcy on eigenspace representations--that is, representations on resolution areas of invariant differential equations. recognized for his top quality expositions, Helgason obtained the 1988 Steele Prize for his prior books Differential Geometry, Lie teams and Symmetric areas and teams and Geometric research. Containing routines (with options) and references to extra effects, this revised variation will be appropriate for complex graduate classes in glossy necessary geometry, research on Lie teams, and illustration idea of Lie teams.
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