A theorem on the Schwartz space of a reductive Lie group
AUTOR(ES)
Arthur, James
RESUMO
The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group. To this end we define a topological vector space, [unk](Ĝ), in terms of the classes of irreducible unitary representations of G, which plays role of a dual Schwartz space. Our main theorem then asserts that the usual L2 Fourier transform, when restricted to functions in the Schwartz space, [unk](G) defined by Harish-Chandra, provides a topological isomorphism from [unk](G) onto [unk](Ĝ).
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=388800Documentos Relacionados
- A recíproca do teorema de Denjoy-Schwartz
- AUTOMORPHIC FORMS ON A SEMISIMPLE LIE GROUP*
- SPHERICAL FUNCTIONS ON A SEMISIMPLE LIE GROUP
- ON THE PLANCHEREL FORMULA FOR THE RIGHT-INVARIANT FUNCTIONS ON A SEMISIMPLE LIE GROUP
- APPLICATION OF HILBERT SPACE METHODS TO LIE GROUPS ACTING ON A DIFFERENTIABLE MANIFOLD