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Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups


Authors: Bruce K. Driver, Nathaniel Eldredge and Tai Melcher
Journal: Trans. Amer. Math. Soc. 368 (2016), 989-1022
MSC (2010): Primary 58J35; Secondary 58J65, 60B15
Published electronically: June 11, 2015
MathSciNet review: 3430356
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Abstract: We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous with respect to a certain product of Gaussian and Lebesgue measures, that the heat kernel is quasi-invariant under translation by the Cameron-Martin subgroup, and that the Radon-Nikodym derivative is Malliavin smooth.


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Additional Information

Bruce K. Driver
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093
Email: bdriver@math.ucsd.edu

Nathaniel Eldredge
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853 – and – School of Mathematical Sciences, University of Northern Colorado, Greeley, Colorado 80639
Email: neldredge@unco.edu

Tai Melcher
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: melcher@virginia.edu

DOI: https://doi.org/10.1090/tran/6461
Keywords: Heisenberg group, hypoelliptic, heat kernel, smooth measures
Received by editor(s): December 12, 2013
Published electronically: June 11, 2015
Additional Notes: The first author’s research was supported in part by NSF Grant DMS-1106270.
The second author’s research was supported in part by NSF Grant DMS-0739164.
The third author’s research was supported in part by NSF Grants DMS-0907293 and DMS-1255574.
Article copyright: © Copyright 2015 American Mathematical Society