A plancherel formula for representative functions on semisimple lie groups

摘要

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