The heat kernel for generalized Heisenberg groups

DOI10.1007/BF02921603zbMath0897.43007OpenAlexW2019789100MaRDI QIDQ1387676

Jennifer Randall

Publication date: 6 October 1998

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921603

zbMATH Keywords

fundamental solution\(L^p\)-estimatesheat kernelheat semigroup\(H\)-type groupgeneralized Heisenberg groupanalytic extension

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Analysis on other specific Lie groups (43A80) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (17)

Spectral multipliers on 2-step groups: topological versus homogeneous dimension ⋮ Estimations Asymptotiques du Noyau de la Chaleur Pour L'opérateur de Grushin ⋮ Riesz transforms on groups of Heisenberg type ⋮ Extension problem and fractional operators: semigroups and wave equations ⋮ Asymptotics for the heat kernel on H-type groups ⋮ Functional calculus for infinitesimal generators of holomorphic semigroups ⋮ Gradient estimates for the heat kernels in higher dimensional Heisenberg groups ⋮ Heat kernels for a class of hybrid evolution equations ⋮ Precise estimates for the subelliptic heat kernel on H-type groups ⋮ Centered Hardy-Littlewood maximal functions on Heisenberg type groups ⋮ UNIQUENESS OF SOLUTIONS TO SCHRÖDINGER EQUATIONS ON -TYPE GROUPS ⋮ Heat kernel transform on nilmanifolds associated to H-type groups ⋮ Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups ⋮ Unnamed Item ⋮ Hartman-Watson distribution and hyperbolic-like heat kernels ⋮ Gradient estimates for the subelliptic heat kernel on H-type groups ⋮ AN UNCERTAINTY PRINCIPLE FOR SOLUTIONS OF THE SCHRÖDINGER EQUATION ON -TYPE GROUPS

Cites Work

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• Hardy-Littlewood theory for semigroups
• The Radon transform
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• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Hypoelliptic second order differential equations
• Semi-Groups of Measures on Lie Groups
• Commutative Algebras of Invariant Functions on Groups of Heisenberg Type
• The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
• Heat kernels for class 2 nilpotent groups
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• On a Generalisation of the Laplace Transformation

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