Abstract
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.
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M. Gordina was supported in part by NSF Grant DMS-1007496, Michler fellowship. T. Melcher was supported in part by NSF Grant DMS-0907293.
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Gordina, M., Melcher, T. A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups. Probab. Theory Relat. Fields 155, 379–426 (2013). https://doi.org/10.1007/s00440-011-0401-4
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DOI: https://doi.org/10.1007/s00440-011-0401-4