The Trace Paley Wiener Theorem for Schwartz Functions
نویسندگان
چکیده
on 11temp (G(F)) . The object of this note is to characterize the image of the map. Results of this nature are well known. The case of the Hecke algebra on G(F), which is in fact more difficult, was established in [3] and [5]. A variant of the problem for the smooth functions of compact support on a real group was solved in [4]. For the Schwartz space, one has a choice of several possible approaches. We shall use the characterization of the operator valued Fourier transform f (f), f EC(G(F)), which was solved separately for real and p-adic groups [2], [9, Part B]. (See also [6, Lemma 5.2].) Irreducible tempered representations occur as constituents of induced representations
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