A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups |
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Authors: | Maria Gordina Tai Melcher |
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Institution: | 1. Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA 2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22903, USA
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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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