Analytic factorization of Lie group representations
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Analytic factorization of Lie group representations. / Gimperlein, Heiko; Krötz, Bernhard ; Lienau, Christoph.
I: Journal of Functional Analysis, Bind 262, Nr. 2, 2012, s. 667-681.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
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