By Sigurdur Helgason
This ebook provides the 1st systematic exposition of geometric research on Riemannian symmetric areas and its courting to the illustration concept of Lie teams. The ebook begins with sleek fundamental geometry for double fibrations and treats numerous examples intimately. After discussing the speculation of Radon transforms and Fourier transforms on symmetric areas, inversion formulation, and diversity theorems, Helgason examines purposes to invariant differential equations on symmetric areas, lifestyles theorems, and particular resolution formulation, fairly strength concept and wave equations. The canonical multitemporal wave equation on a symmetric house is incorporated. The ebook concludes with a bankruptcy on eigenspace representations--that is, representations on resolution areas of invariant differential equations. recognized for his top of the range expositions, Helgason bought the 1988 Steele Prize for his past books Differential Geometry, Lie teams and Symmetric areas and teams and Geometric research. Containing routines (with suggestions) and references to additional effects, this revised version will be appropriate for complex graduate classes in sleek necessary geometry, research on Lie teams, and illustration idea of Lie teams.
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