The heat equation for the Hermite operator on the Heisenberg group
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Publication:2574439
DOI10.14492/hokmj/1285766229zbMath1084.35027OpenAlexW2033927946MaRDI QIDQ2574439
Publication date: 21 November 2005
Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.14492/hokmj/1285766229
Hermite functionsWigner transformsWeyl transforms\(L^p-L^2\) estimatesWeyl-Heisenberg groupsHermite subgroups
One-parameter semigroups and linear evolution equations (47D06) Heat equation (35K05) Initial value problems for second-order parabolic equations (35K15) Pseudodifferential operators (47G30)
Related Items (25)
Correction to: ``Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians ⋮ The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator ⋮ \( Q_\alpha^{- 1}\) spaces for Hermite operator and their applications in a class of Hermite-dissipative equations ⋮ Hierarchical Weyl transforms and the heat semigroup of the hierarchical twisted Laplacian ⋮ The heat kernel of the \(\tau \)-twisted Laplacian ⋮ Global Gevrey hypoellipticity for the twisted Laplacian on forms ⋮ The inverse, the heat semigroup, Liouville's theorems and the spectrum for the Grushin operator ⋮ Subgraphs of \(\alpha\)-Hermite BV functions and the rank-one theorem for \(\mathcal{BV}_{\mathcal{H}_{\alpha}}\) ⋮ Capacity \& perimeter from \(\alpha\)-Hermite bounded variation ⋮ The spectrum of the non-self-adjoint twisted Laplacian on \(\mathbb{R}^2\) ⋮ Metaplectic Equivalence of the Hierarchical Twisted Laplacian ⋮ Global Gevrey hypoellipticity for twisted Laplacians ⋮ Weyl transforms and solutions to Schrödinger equations for time-dependent Hermite operators ⋮ Semiclassical limits of the Schrödinger kernels on the \(h\)-Heisenberg group ⋮ Diagonalization of Weyl transforms and heat equations for time-dependent Hermite operators ⋮ Weyl transforms and a degenerate elliptic partial differential equation ⋮ The heat equation for the generalized Hermite and the generalized Landau operators ⋮ On the local well-posedness of the nonlinear heat equation associated to the fractional Hermite operator in modulation spaces ⋮ Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators ⋮ Classes of Degenerate Elliptic Operators in Gelfand-Shilov Spaces ⋮ Weyl Transforms and the Heat Equation for the Sub-Laplacian on the Heisenberg Group ⋮ Eigenfunction expansions in ℝⁿ ⋮ Anisotropic Shubin operators and eigenfunction expansions in Gelfand-Shilov spaces ⋮ Sobolev and variational capacities in the Hermite setting and their applications ⋮ Weyl transforms, the heat kernel and Green function of a degenerate elliptic operator
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