Analytic factorization of Lie group representations

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Heiko Gimperlein, Bernhard Krötz, Christoph Lienau

For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G.
OriginalsprogEngelsk
TidsskriftJournal of Functional Analysis
Vol/bind262
Udgave nummer2
Sider (fra-til)667-681
ISSN0022-1236
DOI
StatusUdgivet - 2012

ID: 45251091