1. The heat equation for the Hermite operator on the Heisenberg group
- Author
-
M. W. Wong
- Subjects
Hermite polynomials ,General Mathematics ,Operator (physics) ,Heisenberg groups ,Mathematical analysis ,Strongly continuous semigroup ,$L^p - L^2$ estimates ,Hermite functions ,Hermite operators ,35K05 ,Wigner transforms,Weyl transforms ,heat equations ,Norm (mathematics) ,Weyl-Heisenberg groups ,Heisenberg group ,Initial value problem ,Heat equation ,localization operators ,Hermite semigroups ,47G30 ,Mathematical physics ,Mathematics - 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 $1\leq p\leq \infty.$
- Published
- 2005