A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups

• 成果类型: Article
• 署名作者: Gordina, Maria; Melcher, Tai
• 署名单位: University of Connecticut; University of Virginia
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0401-4
• 发表日期: 2013
• 页码: 379-426
• 关键词: heat kernel analysis; holomorphic-functions; malliavin calculus; map

摘要

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.