The heat equation for the generalized Hermite and the generalized Landau operators
type: Item
instance of: scholarly article
title: The heat equation for the generalized Hermite and the generalized Landau operators
zbMATH Open document ID: 1226.47043
author: Viorel Catană
published in: Integral Equations and Operator Theory
publication date: 2010-08-23T00:00:00Z
review text: Stimulated by the paper [\textit{M. W. Wong}, Hokkaido Math. J. 34, No.~2, 393--404 (2005; Zbl 1084.35027)], the author gives a representation of the strongly continuous semigroups generated by a class of generalized Hermite operators. A similar result is also given for the strongly continuous semigroups generated by some generalized Landau operators based on the work [\textit{M. A. de Gosson}, Commun. Partial Differ. Equations 33, No.~11, 2096--2104 (2008; Zbl 1159.35077)].
reviewed by: Jin Liang
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35S10
zbMATH DE Number: 5774242
zbMATH Keywords: generalized Hermite operators
zbMATH Keywords: generalized Landau operatorsWeyl transform
zbMATH Keywords: Fourier-Wigner transform
zbMATH Keywords: Wigner transform
zbMATH Keywords: one-parameter strongly continuous semigroup
MaRDI profile type: Publication
full work available at URL: s00020-009-1737-3
OpenAlex ID: W2127932140
cites work: The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
cites work: Symplectic geometry and quantum mechanics
cites work: Spectral Properties of a Class of Generalized Landau Operators
cites work: Q4725211
cites work: The heat equation for the Hermite operator on the Heisenberg group
cites work: Wavelet transforms and localization operators
DOI: 10.1007/S00020-009-1737-3
description: scientific article; zbMATH DE number 5774242