Spectral Analysis and Geometry of Sub-Laplacian and Related Grushin-type Operators

DOI10.1007/978-3-0348-0024-2_4zbMath1307.58012OpenAlexW167512654MaRDI QIDQ2904901

Chisato Iwasaki, Wolfram Bauer, Kenro Furutani

Publication date: 24 August 2012

Published in: Partial Differential Equations and Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0024-2_4

zbMATH Keywords

latticeHeisenberg groupvector fieldnilpotent Lie groupnilmanifoldSelberg trace formulaheat kernelDirichlet seriesisoperimetric problempseudo-differential operatorsub-LaplacianHörmander conditionEngel groupsub-Riemannian manifoldspectral zeta functionEpstein zeta functionquaternion fieldHopf bundlefree nilpotent Lie groupsub-Riemannian geodesicsdouble fibrationChow conditionGrushin-type operatorsingular Riemannian manifoldbicharacteristic flowhypo-elliptic operator

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Sub-Riemannian geometry (53C17) Subelliptic equations (35H20) Heat kernel (35K08)

Related Items (8)

Complete classification of pseudo \(H\)-type Lie algebras. I ⋮ Trivializable sub-Riemannian structures on spheres ⋮ From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere ⋮ Heat kernels for a class of hybrid evolution equations ⋮ An action function for a higher step Grushin operator ⋮ Fundamental solution of a higher step Grushin type operator ⋮ Spectral zeta function of a sub-Laplacian on product sub-Riemannian manifolds and zeta-regularized determinant ⋮ Spectral zeta function of the sub-Laplacian on two step nilmanifolds

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