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Parametrix for a
semiclassical subelliptic operator
Hart F. Smith |
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Vol. 13 (2020), No. 8, 2375–2398
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Abstract |
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We demonstrate a parametrix construction, together with associated pseudodifferential operator calculus, for an operator of sum-of-squares type with semiclassical parameter. The form of operator we consider includes the generator of kinetic Brownian motion on the cosphere bundle of a Riemannian manifold. Regularity estimates in semiclassical Sobolev spaces are proven by establishing mapping properties for the parametrix. |
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Keywords
subelliptic equations, semiclassical analysis, resonance
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Mathematical Subject Classification 2010
Primary: 35H20
Secondary: 35S05
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Milestones
Received: 13 October 2018
Revised: 27 June 2019
Accepted: 25 September 2019
Published: 28 December 2020
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Authors |
| Hart F. Smith | |
| Department of Mathematics University of Washington Seattle, WA United States |
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