Analytic factorization of Lie group representations

Heiko Gimperlein; Bernhard  Krötz; Christoph Lienau

doi:10.1016/j.jfa.2011.10.002

Analytic factorization of Lie group representations

Heiko Gimperlein, Bernhard Krötz, Christoph Lienau

Institut for Matematiske Fag

5 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Functional Analysis
Vol/bind	262
Udgave nummer	2
Sider (fra-til)	667-681
ISSN	0022-1236
DOI	https://doi.org/10.1016/j.jfa.2011.10.002
Status	Udgivet - 15 jan. 2012

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10.1016/j.jfa.2011.10.002

Citationsformater

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title = "Analytic factorization of Lie group representations",

abstract = "For every moderate growth representation (π, E) of a real Lie group G on a Fr{\'e}chet space, we prove a factorization theorem of Dixmier-Malliavin type for the space of analytic vectors Eω. There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that Eω=Π(A(G))Eω. As a corollary we obtain that Eω coincides with the space of analytic vectors for the Laplace-Beltrami operator on G.",

author = "Heiko Gimperlein and Bernhard Kr{\"o}tz and Christoph Lienau",

year = "2012",

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T1 - Analytic factorization of Lie group representations

AU - Gimperlein, Heiko

AU - Krötz, Bernhard

AU - Lienau, Christoph

PY - 2012/1/15

Y1 - 2012/1/15

N2 - For every moderate growth representation (π, 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 Eω. There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that Eω=Π(A(G))Eω. As a corollary we obtain that Eω coincides with the space of analytic vectors for the Laplace-Beltrami operator on G.

AB - For every moderate growth representation (π, 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 Eω. There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that Eω=Π(A(G))Eω. As a corollary we obtain that Eω coincides with the space of analytic vectors for the Laplace-Beltrami operator on G.

U2 - 10.1016/j.jfa.2011.10.002

DO - 10.1016/j.jfa.2011.10.002

M3 - Journal article

SN - 0022-1236

VL - 262

SP - 667

EP - 681

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Analytic factorization of Lie group representations

Abstract

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