Abstract
For a real linear algebraic group G let \({\mathcal{A}(G)}\) 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 \({\mathcal{A}(G)}\). Since \({\mathcal{A}(G)}\) acts on E for every Fréchet-representation (π, 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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Lienau, C. Analytic Dirac approximation for real linear algebraic groups. Math. Ann. 351, 403–410 (2011). https://doi.org/10.1007/s00208-010-0607-2
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DOI: https://doi.org/10.1007/s00208-010-0607-2