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ORBITAL INTEGRALS ON  REDUCTIVE LIE GROUPS  AND THEIR ALGEBRAS   

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In the study of the theory of irreducible unitary representations, is necessary to analyze and demonstrate diverse results on integral orbital of functions belonging to the cohomology Hi (g, K; V V *), and that it is wanted they belong to the L2(G)-cohomology of their reducible unitary representations called discrete series. Then is necessary consider the Frèchet space I(G), and analyze the 2-integrability to the fibers of the space G/K, in spaces or locally compact components of G/K. For it will be useful the invariance of the corresponding measures of Haar under the actions of Ad(G), and the.