Analytic factorization of Lie group representations
Copyright policy )Analytic factorization of Lie group representations
For every moderate growth representation of a real Lie group G on a Frechet space E, we prove a factorization theorem of Dixmier--Malliavin type for the space of analytic vectors E^��. There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that E^�� = A(G) * E^��. As a corollary we obtain that E^��coincides with the space of analytic vectors for the Laplace--Beltrami operator on G.
14 pages
- University of Hannover Germany
- University of Copenhagen Denmark
- University of Copenhagen Denmark
FOS: Mathematics, Dixmier–Malliavin, 22Exx, Factorization, Analytic vectors, Representation Theory (math.RT), Lie group representation, Analysis, Mathematics - Representation Theory
FOS: Mathematics, Dixmier–Malliavin, 22Exx, Factorization, Analytic vectors, Representation Theory (math.RT), Lie group representation, Analysis, Mathematics - Representation Theory
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