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A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups
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  • Published: 01 December 2011

A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups

  • Maria Gordina1 &
  • Tai Melcher2 

Probability Theory and Related Fields volume 155, pages 379–426 (2013)Cite this article

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  • 2 Citations

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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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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA

    Maria Gordina

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22903, USA

    Tai Melcher

Authors
  1. Maria Gordina
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  2. Tai Melcher
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Corresponding author

Correspondence to Maria Gordina.

Additional information

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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  • Received: 10 June 2011

  • Revised: 13 November 2011

  • Published: 01 December 2011

  • Issue Date: February 2013

  • DOI: https://doi.org/10.1007/s00440-011-0401-4

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Keywords

  • Heisenberg group
  • Heat kernel
  • Subelliptic operator
  • Taylor map
  • Holomorphic function

Mathematics Subject Classification (2000)

  • Primary 35H10
  • 43A15
  • Secondary 58J65
  • 22E65
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