So far we have dealt mostly with the Iwasawa decomposition from various points of view: projection on invariant differential operators, spherical functions, etc. Already in studying spherical functions, the action of K on the left was crucial. In the present chapter, and the next two, we deal with an alternate continuation of Chapter III, independent of the Gelfand-Naimark decomposition, namely we deal with the polar decomposition G = KAK. We also complement Chapter IV, §6 in §3.
KeywordsHaar Measure Spherical Function Regular Element Polar Decomposition Linear Isomorphism
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