Analytic factorization of Lie group representations

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Standard

Analytic factorization of Lie group representations. / Gimperlein, Heiko; Krötz, Bernhard ; Lienau, Christoph.

In: Journal of Functional Analysis, Vol. 262, No. 2, 2012, p. 667-681.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Gimperlein, H, Krötz, B & Lienau, C 2012, 'Analytic factorization of Lie group representations', Journal of Functional Analysis, vol. 262, no. 2, pp. 667-681. https://doi.org/10.1016/j.jfa.2011.10.002

APA

Gimperlein, H., Krötz, B., & Lienau, C. (2012). Analytic factorization of Lie group representations. Journal of Functional Analysis, 262(2), 667-681. https://doi.org/10.1016/j.jfa.2011.10.002

Vancouver

Gimperlein H, Krötz B, Lienau C. Analytic factorization of Lie group representations. Journal of Functional Analysis. 2012;262(2):667-681. https://doi.org/10.1016/j.jfa.2011.10.002

Author

Gimperlein, Heiko ; Krötz, Bernhard ; Lienau, Christoph. / Analytic factorization of Lie group representations. In: Journal of Functional Analysis. 2012 ; Vol. 262, No. 2. pp. 667-681.

Bibtex

@article{0a0f3aacf1ac435087af220e7d1ab9e0,
title = "Analytic factorization of Lie group representations",
abstract = "For every moderate growth representation (p,E)(p,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 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.",
author = "Heiko Gimperlein and Bernhard Kr{\"o}tz and Christoph Lienau",
year = "2012",
doi = "10.1016/j.jfa.2011.10.002",
language = "English",
volume = "262",
pages = "667--681",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "2",

}

RIS

TY - JOUR

T1 - Analytic factorization of Lie group representations

AU - Gimperlein, Heiko

AU - Krötz, Bernhard

AU - Lienau, Christoph

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1016/j.jfa.2011.10.002

DO - 10.1016/j.jfa.2011.10.002

M3 - Journal article

VL - 262

SP - 667

EP - 681

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -

ID: 45251091