Heat kernel analysis on infinite-dimensional Heisenberg groups |
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Authors: | Bruce K Driver Maria Gordina |
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Institution: | a Department of Mathematics, 0112, University of California, San Diego, La Jolla, CA 92093-0112, USA b Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA |
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Abstract: | We introduce a class of non-commutative Heisenberg-like infinite-dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the corresponding heat kernel measures, {νt}t>0, are also studied. We show that these heat kernel measures admit: (1) Gaussian like upper bounds, (2) Cameron-Martin type quasi-invariance results, (3) good Lp-bounds on the corresponding Radon-Nikodym derivatives, (4) integration by parts formulas, and (5) logarithmic Sobolev inequalities. The last three results heavily rely on the boundedness of the Ricci tensor. |
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Keywords: | Heisenberg group Heat kernel Quasi-invariance Logarithmic Sobolev inequality |
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