Fourier Analysis on GL(n,R).
Two problems of Fourier analysis on GL(n,R) are studied. The first concerns the decomposition of the additive Fourier operator in terms of the group representation theory of G. The second concerns the analytic continuation of certain zeta-functions defined on G. It is found that the generalized Gamma functions of Gelfand and Graev arise naturally in the solution of both these problems.
PRINCETON UNIVERSITY.
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Gelbart