Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T05:35:05.140Z Has data issue: false hasContentIssue false
  • English
  • Français

Semiclassical Limits of Heat Kernels of Laplacians on theh-Heisenberg Group

Published online by Cambridge University Press:  28 January 2013

T. Kagawa  and
M. W. Wong
T. Kagawa
Affiliation:
Department of Mathematics, Tokyo University of Science, 2641 Yamazaki Noda, Chiba (278-8510), Japan
M. W. Wong*
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street Toronto, Ontario M3J 1P3, Canada
*
∗Corresponding author. E-mail: [email protected]. This research has been supported by a discovery grantfrom the Natural Sciences and Engineering Research Council of Canada.
Get access

Abstract

We construct the heat kernels of the sub-Laplacian and the Laplacian on theh-Heisenberg group and compute the limits as h → 0 ofthe heat kernels.

Keywords

h-Heisenberg groupsub-LaplacianLaplacianFourier-Wigner transformsHermite functionsheat kernelssemiclassical limits
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 132 - 142
Copyright
© EDP Sciences, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

A. Dasgupta, M. W. Wong.Weyl transforms and the heat equation for the sub-Laplacian on the Heisenberg group, in New Developments in Pseudo-Differential Operators. Operator Theory : Advances and Applications, 189, Birkhäuser, 2009, 33–42.
Dasgupta, A., Wong, M. W.. The semigroup and the inverse of the Laplacian on the Heisenberg group. CUBO A Mathematical Journal 12 (2010), 83–97. CrossRefGoogle Scholar
Gaveau, B.. Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents. Acta Math. 139 (1977), 95–153. CrossRefGoogle Scholar
Hulanicki, A., The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group. Studia Math. 56 (1976), 165–173. CrossRefGoogle Scholar
S. Thangavelu. Harmonic Analysis on the Heisenberg Group. Birkhäuser, 1998.
M. W. Wong. Weyl Transforms. Springer-Verlag, 1998.
Wong, M. W.. Weyl transforms, the heat kernel and Green function of a degenerate elliptic operator. Ann. Global Anal. Geom. 28 (2005), 271–283. CrossRefGoogle Scholar
M. W. Wong. Weyl transforms and convolution operators on the Heisenberg group in Pseudo-Differential Operators and Related Topics. Operator Theory : Advances and Applications 164 Birkhäuser, 2005, 115–120.