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The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group.

SupposethatGisaLiegroup.whichforthepurposeofthisintroduction,wetaketobearealformofasimplyconnectedcomplexsemisimplegroup.Supposethatsquareintegrablere

Selberg迹公式，The Selberg trace formula leads naturally to the study of certain tempered distributions on reductive groups defined over local fields. An