Analytic factorization of Lie group representations
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Journal of Functional Analysis |
Volume | 262 |
Issue number | 2 |
Pages (from-to) | 667-681 |
ISSN | 0022-1236 |
DOIs | |
Publication status | Published - 2012 |
ID: 45251091