By Sigurdur Helgason
This publication offers the 1st systematic exposition of geometric research on Riemannian symmetric areas and its courting to the illustration conception of Lie teams. The ebook begins with sleek critical 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 functions to invariant differential equations on symmetric areas, life theorems, and particular answer formulation, fairly power conception 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 fine 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 workouts (with options) and references to additional effects, this revised variation will be compatible for complicated graduate classes in sleek crucial geometry, research on Lie teams, and illustration concept of Lie teams.
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