Asymptotics for some Green kernels on the Heisenberg group and the Martin boundary

DOI10.1007/BF01457504zbMath0639.31005OpenAlexW1965733462MaRDI QIDQ1100316

Detlef Müller, Hermann Hueber

Publication date: 1989

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164496

zbMATH Keywords

heat equationHeisenberg groupMartin boundaryfundamental solutionharmonic functionasymptotic behaviourMartin compactificationLapace-Kohn operator

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Heat equation (35K05) Martin boundary theory (31C35) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

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Estimations optimales du noyau de la chaleur sur les groupes de type Heisenberg, Estimations Asymptotiques du Noyau de la Chaleur Pour L'opérateur de Grushin, Carnot Geometry and the Resolvent of the Sub-Laplacian for the Heisenberg Group, Asymptotics for the heat kernel on H-type groups, Asymptotic estimates for the heat kernel on Heisenberg groups, The Martin boundary of a free product of abelian groups, On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group, Martin compactification and asymptotics of Green functions for Schrödinger operators with anisotropic potentials, Precise estimates for the subelliptic heat kernel on H-type groups, The subelliptic heat kernels on \(\mathbf{SL}(2,\mathbb{R})\) and on its universal covering \(\widetilde{\mathbf{SL}(2,\mathbb{R})}\): Integral representations and some functional inequalities, On estimates for the Besov norms of solutions to 3D subelliptic equations, Group classification of semilinear Kohn-Laplace equations, Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups*, Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg, Asymptotics for certain harmonic functions and the Martin compactification on the quaternionic Heisenberg group, Conservations laws for critical Kohn-Laplace equations on the Heisenberg group, Coercive inequalities on metric measure spaces

Cites Work

• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Hypoelliptic second order differential equations
• Caracterisation des operateurs hypoelliptiques homogenes
• Hypoellipticity on the Heisenberg Group-Representation-Theoretic Criteria
• The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
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