By Sigurdur Helgason

This booklet offers the 1st systematic exposition of geometric research on Riemannian symmetric areas and its courting to the illustration idea of Lie teams. The e-book begins with sleek critical geometry for double fibrations and treats a number of examples intimately. After discussing the idea of Radon transforms and Fourier transforms on symmetric areas, inversion formulation, and variety theorems, Helgason examines functions to invariant differential equations on symmetric areas, life theorems, and particular answer formulation, really strength concept and wave equations. The canonical multitemporal wave equation on a symmetric area is integrated. The publication concludes with a bankruptcy on eigenspace representations--that is, representations on answer areas of invariant differential equations. recognized for his fine quality expositions, Helgason acquired the 1988 Steele Prize for his past books Differential Geometry, Lie teams and Symmetric areas and teams and Geometric research. Containing workouts (with recommendations) and references to extra effects, this revised version will be compatible for complex graduate classes in glossy critical geometry, research on Lie teams, and illustration concept of Lie teams.

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