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- W2950787931 abstract "We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like 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 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." @default.
- W2950787931 created "2019-06-27" @default.
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- W2950787931 date "2008-09-29" @default.
- W2950787931 modified "2023-09-23" @default.
- W2950787931 title "Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups" @default.
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