The Paley-Wiener-Levinson theorem revisited
نویسندگان
چکیده
منابع مشابه
Trace Paley - Wiener Theorem
w Statement of the theorem 1.1. Let G be a reductive p-adic group. A smooth representation (~', E) of the group G on a complex vector space E is called a G-module. Usually we shorten the notation and write w or E. Let d~(G) be the category of G-modules, Irr G the set of equivalence classes of irreducible G-modules, and R (G) the Grothendieck group of G-modules of fnite length; R(G) is a free ab...
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One of the more beautiful results in the harmonic analysis of symmetric spaces is the Helgason Theorem, which states that on a Riemannian symmetric space X = G=K, a function is annihilated by the algebra DG(X) of all G-invariant di erential operators if and only if it is the Poisson integral of a hyperfunction over the \maximal" boundary. (See [KKMOOT].) If X is a Hermitian symmetric space, the...
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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 appro...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1997
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171297000306