For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.

Iwasawa Decomposition and Positivity 
Invariant Differential Operators and the Iwasawa Direct Image 
Characters, Eigenfunctions, Spherical Kernel and W-Invariance 
Convolutions, Spherical Functions and the Mellin Transform 
Gelfand-Naimark Decomposition and the Harish-Chandra --Function
Polar Decomposition 
The Casimir Operator 
The Harish-Chandra Series for Eigenfunctions of Casimir 
General Inversion 
The Harish-Chandra Schwartz Space (HCS) and Anker's Proof of Inversion 
Tube Domains and the L^1 (Even L^p) HCS Spaces * SL_n(C)

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