The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator

DOI10.1007/978-3-0348-0049-5_9zbMath1266.47068OpenAlexW122210513MaRDI QIDQ2904927

Viorel Catană

Publication date: 24 August 2012

Published in: Pseudo-Differential Operators: Analysis, Applications and Computations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0049-5_9

zbMATH Keywords

heat kernelGreen functionWigner transformultracontractivityhypercontractivityHermite operatorWeyl transformglobal hypoellipticityFourier-Wigner transform

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Eigenvalue problems for linear operators (47A75) General theory of partial differential operators (47F05) PDEs in connection with quantum mechanics (35Q40)

Related Items (1)

The generalized twisted bi-Laplacian and its spectral properties

Cites Work

• Wavelet transforms and localization operators
• The heat equation for the generalized Hermite and the generalized Landau operators
• Weyl transforms
• Harmonic analysis on the Heisenberg group
• An algebra of pseudodifferential operators and quantum mechanics in phase space
• 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
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