By Sigurdur Helgason
This e-book provides the 1st systematic exposition of geometric research on Riemannian symmetric areas and its dating to the illustration idea of Lie teams. The publication starts off with smooth essential 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 diversity theorems, Helgason examines functions to invariant differential equations on symmetric areas, lifestyles theorems, and specific answer formulation, relatively capability concept and wave equations. The canonical multitemporal wave equation on a symmetric house is integrated. The booklet concludes with a bankruptcy on eigenspace representations--that is, representations on resolution areas of invariant differential equations. recognized for his high quality expositions, Helgason acquired the 1988 Steele Prize for his prior books Differential Geometry, Lie teams and Symmetric areas and teams and Geometric research. Containing routines (with recommendations) and references to extra effects, this revised variation will be appropriate for complex graduate classes in sleek fundamental geometry, research on Lie teams, and illustration concept of Lie teams.
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