The inverse, the heat semigroup, Liouville's theorems and the spectrum for the Grushin operator

DOI10.1007/s11868-010-0016-zzbMath1223.47048OpenAlexW2160897078MaRDI QIDQ619635

Shahla Molahajloo, Aparajita Dasgupta, Man-Wah Wong

Publication date: 25 January 2011

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11868-010-0016-z

zbMATH Keywords

Sobolev spacescontinuous spectrumeigenvaluesspectrumHermite functionsinversesGrushin operatorLiouville's theoremheat semigroupsparametrized Hermite operators

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) General theory of partial differential operators (47F05) Pseudodifferential operators (47G30)

Related Items

Images of some subspaces of \(L^2(\mathbb{R}^m)\) under Grushin and Hermite semigroup ⋮ The Heston Riemannian distance function

Cites Work

• Hypoelliptic second order differential equations
• The heat equation for the Hermite operator on the Heisenberg group
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• On the essential spectrum of partial differential boundary problems
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Fourier–Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
• Sur une classe d'opérateurs elliptiques dégénérés
• ON A CLASS OF ELLIPTIC PSEUDODIFFERENTIAL OPERATORS DEGENERATE ON A SUBMANIFOLD
• ON A CLASS OF HYPOELLIPTIC OPERATORS
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