Analytic factorization of Lie group representations

TY - JOUR

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 -