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Titlebook: Spherical Inversion on SLn(R); Jay Jorgenson,Serge Lang Book 2001 Springer-Verlag New York, Inc. 2001 Convexity.algebra.differential opera

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Iwasawa Decomposition and Positivity,dra concerning this partial ordering. The theorem compares the size of the A-component in the Iwasawa and polar decompositions. Jacobian computations and basic effects of polar decomposition on differential operators will be given in Chapter VI.
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Gelfand-Naimark Decomposition and the Harish-Chandra ,-Function,This chapter continues the integral representation of spherical functions. Most of it is due to Harish-Chandra [Har 58a], who recognized and developed the role of . = .. in his theory of spherical inversion. This chapter develops the information which arises from the Gelfand-Naimark decomposition.
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The Casimir Operator,To begin with, this chapter provides an example for an especially important invariant differential operator, and its direct image on . with respect to the Iwasawa decomposition and the polar decomposition. It is independent of Chapter V and is a direct continuation of Chapter VI.
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978-1-4419-2883-2Springer-Verlag New York, Inc. 2001
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