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 $1\leq p\leq \infty.$
Citation
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
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