Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups

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dc.creatorDriver, Bruce
dc.creatorGordina, Maria
dc.date2008-09-29
dc.date.accessioned2026-07-07T10:06:11Z
dc.date.available2026-07-07T10:06:11Z
dc.descriptionWe 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 $μ$ 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 $L^{2}(ν)$-closure of holomorphic polynomials by their values on the Cameron-Martin subgroup.
dc.identifierhttps://arxiv.org/abs/0809.4979
dc.identifierhttp://arxiv.org/abs/0809.4979
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170240
dc.subjectProbability
dc.subjectDifferential Geometry
dc.subject35K05, 43A15, 58G32
dc.titleSquare integrable holomorphic functions on infinite-dimensional Heisenberg type groups
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