This book gives the first systematic exposition of geometric analysis on
Riemannian symmetric spaces and its relationship to the representation
theory of Lie groups. The book starts with modern integral geometry for
double fibrations and treats several examples in detail. After discussing
the theory of Radon transforms and Fourier transforms on symmetric spaces,
inversion formulas, and range theorems, Helgason examines applications to
invariant differential equations on symmetric spaces, existence theorems,
and explicit solution formulas, particularly potential theory and wave
equations. The canonical multitemporal wave equation on a symmetric space
is included. The book concludes with a chapter on eigenspace
representations—that is, representations on solution spaces of invariant
differential equations. Known for his high-quality expositions, Helgason
received the 1988 Steele Prize for his earlier books Differential
Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric
Analysis. Containing exercises (with solutions) and references to further
results, this revised edition would be suitable for advanced graduate
courses in modern integral geometry, analysis on Lie groups, and
representation theory of Lie groups.
Readership
Graduate students and research mathematicians interested in
analysis on symmetric spaces and the representation theory of Lie
groups.