Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups

• 成果类型: Article
• 署名作者: Driver, Bruce K.; Gordina, Maria
• 署名单位: University of California System; University of California San Diego; University of Connecticut
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0213-y
• 发表日期: 2010
• 页码: 481-528
• 关键词: heat kernel analysis; taylor map

摘要

We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure mu on these groups are studied. In particular, we establish a unitary equivalence between the square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the Lie algebra of this class of groups. Using quasi-invariance of the heat kernel measure, we also construct a skeleton map which characterizes globally defined functions from the L (2)(nu)-closure of holomorphic polynomials by their values on the Cameron-Martin subgroup.