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June 2005 The heat equation for the Hermite operator on the Heisenberg group
M. W. WONG
Hokkaido Math. J. 34(2): 393-404 (June 2005). DOI: 10.14492/hokmj/1285766229

Abstract

We give a formula for the one-parameter strongly continuous semigroup $e^{-tL},\,t>0$, generated by the Hermite operator $L$ on the Heisenberg group $\H1$ in terms of Weyl transforms, and use it to obtain an $L^2$ estimate for the solution of the initial value problem for the heat equation governed by $L$ in terms of the $L^p$ norm of the initial data for $1\leq p\leq \infty.$

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M. W. WONG. "The heat equation for the Hermite operator on the Heisenberg group." Hokkaido Math. J. 34 (2) 393 - 404, June 2005. https://doi.org/10.14492/hokmj/1285766229

Information

Published: June 2005
First available in Project Euclid: 29 September 2010

zbMATH: 1084.35027
MathSciNet: MR2159004
Digital Object Identifier: 10.14492/hokmj/1285766229

Subjects:
Primary: 35K05
Secondary: 47G30

Rights: Copyright © 2005 Hokkaido University, Department of Mathematics

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Vol.34 • No. 2 • June 2005
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