By Sigurdur Helgason
This publication provides the 1st systematic exposition of geometric research on Riemannian symmetric areas and its courting to the illustration concept of Lie teams. The e-book begins with sleek essential geometry for double fibrations and treats numerous 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, lifestyles theorems, and particular resolution formulation, rather power conception and wave equations. The canonical multitemporal wave equation on a symmetric house is integrated. The e-book concludes with a bankruptcy on eigenspace representations--that is, representations on answer areas of invariant differential equations. identified for his high quality expositions, Helgason bought the 1988 Steele Prize for his prior books Differential Geometry, Lie teams and Symmetric areas and teams and Geometric research. Containing routines (with strategies) and references to extra effects, this revised version will be compatible for complex graduate classes in glossy fundamental geometry, research on Lie teams, and illustration conception of Lie teams.
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