A subelliptic Taylor isomorphism on infinitedimensional Heisenberg groups
Abstract
Let $G$ denote an infinitedimensional Heisenberglike group, which is a class of infinitedimensional 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 "CameronMartin" Lie subalgebra. The isomorphism defining the equivalence is given as a composition of restriction and Taylor maps.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 DOI:
 10.48550/arXiv.1106.1970
 arXiv:
 arXiv:1106.1970
 Bibcode:
 2011arXiv1106.1970G
 Keywords:

 Mathematics  Probability;
 35H10 43A15 (Primary) 58J65 22E65 (Secondary)
 EPrint:
 Initially posted in June 2011, with minor corrections in November 2011