A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups

Abstract

Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure which is formally subelliptic, in the sense that all appropriate finite dimensional projections are smooth measures. We prove a unitary equivalence between a subclass of these square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the "Cameron-Martin" Lie subalgebra. The isomorphism defining the equivalence is given as a composition of restriction and Taylor maps.

arXiv commentInitially posted in June 2011, with minor corrections in November 2011

References in corpus (1)

• Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups