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Journal of Lie Theory 23 (2013), No. 2, 493--505
Copyright Heldermann Verlag 2013

A Plancherel Formula for Representative Functions on Semisimple Lie Groups

Robert W. Donley, Jr.
344 Grove Street, #20, Jersey City, NJ 07306, U.S.A.

A Plancherel formula is given for representative functions on a connected semisimple Lie group G. Since the matrix coefficients for the irreducible finite-dimensional representations are not necessarily square-integrable, an alternative to the Schur Orthogonality Relations is given using invariant differential operators. The corresponding operator analysis is summarized.

Keywords: Semisimple Lie group, Schur orthogonality relations, matrix coefficient, representative function, Plancherel formula.

MSC: 22E46

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