Analytic Dirac approximation for real linear algebraic groups

Details Analytic Dirac approximation for real linear algebraic groups Analytic Dirac approximation for real linear algebraic groups

2010-02-24

arxiv.org/abs/1002.4462v1

Mathematics

Representation Theory

7 pages

Scientific paper

For a real linear algebraic group G let A(G) be the algebra of analytic vectors for the left regular representation of G on the space of superexponentially decreasing functions. We present an explicit Dirac sequence in A(G). Since A(G) acts on E for every Frechet-representation (\pi,E) of moderate growth, this yields an elementary proof of a result of Nelson that the space of analytic vectors is dense in E.

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