Weyl Transforms and the Heat Equation for the Sub-Laplacian on the Heisenberg Group

DOI10.1007/978-3-7643-8969-7_3zbMath1173.47029OpenAlexW73953985MaRDI QIDQ3613195

Aparajita Dasgupta, Man-Wah Wong

Publication date: 12 March 2009

Published in: New Developments in Pseudo-Differential Operators (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-7643-8969-7_3

zbMATH Keywords

Sobolev spacesHeisenberg groupheat kernelHermite functionssub-Laplaciantwisted LaplacianWeyl transformsFourier-Wigner transforms

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Pseudodifferential operators (47G30) Subelliptic equations (35H20)

Related Items (6)

Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane ⋮ Hierarchical Weyl transforms and the heat semigroup of the hierarchical twisted Laplacian ⋮ Semiclassical limits of the Schrödinger kernels on the \(h\)-Heisenberg group ⋮ Diagonalization of Weyl transforms and heat equations for time-dependent Hermite operators ⋮ The spectrum of the sub-Laplacian on the Heisenberg group ⋮ My mathematical connections with Luigi Rodino

Cites Work

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• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Weyl transforms
• Harmonic analysis on the Heisenberg group
• An introduction to the uncertainty principle. Hardy's theorem on Lie groups. With a foreword by Gerald B. Folland
• Global solutions of semilinear heat equations in Hilbert spaces
• The heat equation for the Hermite operator on the Heisenberg group
• Weyl transforms, the heat kernel and Green function of a degenerate elliptic operator
• The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
• Positive definite temperature functions on the Heisenberg group
• The Twisted Laplacian on ℂⁿand the Sub-Laplacian on H_n

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