The Twisted Laplacian on ℂnand the Sub-Laplacian on Hn

DOI10.1080/03605300500455966zbMath1101.35027OpenAlexW1997857535MaRDI QIDQ5491383

Jingzhi Tie

Publication date: 11 October 2006

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500455966

zbMATH Keywords

fundamental solutionspectrumeigenfunctionsfinite speed of propagationsub-Laplacians

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Fundamental solutions to PDEs (35A08) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Potentials and capacities on other spaces (31C15) Subelliptic equations (35H20)

Related Items (12)

The heat kernel of the \(\tau \)-twisted Laplacian ⋮ Global Gevrey hypoellipticity for the twisted Laplacian on forms ⋮ Concrete \(L^2\)-spectral analysis of a bi-weighted \(\Gamma \)-automorphic twisted Laplacian ⋮ Sub-Riemannian Geometry and Hypoelliptic Operators ⋮ Metaplectic Equivalence of the Hierarchical Twisted Laplacian ⋮ Weyl transforms and solutions to Schrödinger equations for time-dependent Hermite operators ⋮ Diagonalization of Weyl transforms and heat equations for time-dependent Hermite operators ⋮ Weyl Transforms and the Heat Equation for the Sub-Laplacian on the Heisenberg Group ⋮ A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group ⋮ On concrete spectral properties of a twisted Laplacian associated with a central extension of the real Heisenberg group ⋮ Sharp estimates for the Schrödinger equation associated with the twisted Laplacian ⋮ Pseudo-differential Operators on Non-isotropic Heisenberg Groups with Multi-dimensional Centers

Cites Work

• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Weyl transforms
• Harmonic analysis on the Heisenberg group
• Calculus on Heisenberg Manifolds. (AM-119)
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
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