Analytic factorization of Lie group representations

被引：6

作者：

Gimperlein, Heiko ^{[2
]}

Kroetz, Bernhard ^{[1
]}

Lienau, Christoph ^{[1
]}

机构：

[1] Leibniz Univ Hannover, D-30167 Hannover, Germany

[2] Dept Math Sci, DK-2100 Copenhagen O, Denmark

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 02期

关键词：

Dixmier-Malliavin; Factorization; Analytic vectors; Lie group representation;

D O I：

10.1016/j.jfa.2011.10.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For every moderate growth representation (pi, E) of a real Lie group G on a Frechet space, we prove a factorization theorem of Dixmier-Malliavin type for the space of analytic vectors E(omega). There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that E(omega) = Pi(A(G))E(omega). As a corollary we obtain that E(omega) coincides with the space of analytic vectors for the Laplace-Beltrami operator on G. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：667 / 681

页数：15

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