Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one

DOI10.1016/S0007-4497(01)01099-5zbMath0994.60075WikidataQ126838462 ScholiaQ126838462MaRDI QIDQ5956292

Hiroyuki Matsumoto

Publication date: 20 February 2002

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Mathematics Subject Classification ID

Brownian motion (60J65) Fundamental solutions to PDEs (35A08) Heat equation (35K05) Diffusion processes (60J60) Differential geometry of symmetric spaces (53C35)

Related Items (14)

Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces ⋮ Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on the Siegel domains and complex hyperbolic spaces ⋮ Hyperbolic Green function estimates ⋮ Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula ⋮ Improved Caffarelli-Kohn-Nirenberg inequalities in unit ball and sharp constants in dimension three ⋮ Explicit formulas of the heat kernel on the quaternionic projective spaces ⋮ Potential characterizations of geodesic balls on hyperbolic spaces: a moving plane approach ⋮ On potential theory of hyperbolic Brownian motion with drift ⋮ Large deviations for the radial processes of the Brownian motions on hyperbolic spaces ⋮ Fundamental solutions and Gegenbauer expansions of Helmholtz operators in Riemannian spaces of constant curvature ⋮ Centered Hardy--Littlewood maximal function on hyperbolic spaces ⋮ Hartman-Watson distribution and hyperbolic-like heat kernels ⋮ Green's functions of Paneitz and GJMS operators on hyperbolic spaces and sharp Hardy-Sobolev-Maz'ya inequalities on half spaces ⋮ Bessel bridge representation for the heat kernel in hyperbolic space

Cites Work

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