Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula

DOI10.1016/j.jfa.2006.10.005zbMath1118.58019OpenAlexW2052266374MaRDI QIDQ880106

Hiroyuki Matsumoto

Publication date: 10 May 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.10.005

zbMATH Keywords

Brownian motionSelberg trace formulaheat kernelhyperbolic planehorizontal liftde Rham-Kodaira LaplacianPoincaré upper half plane

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Irrationality; linear independence over a field (11J72)

Cites Work

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• Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Brownian motion on the hyperbolic plane and Selberg trace formula
• On some exponential functionals of Brownian motion
• Fourier coefficients of the resolvent for a Fuchsian group.
• Analyse harmonique des formes différentielles sur l'espace hyperbolique réel II. Transformation de Fourier sphérique et applications
• Analyse harmonique des formes différentielles sur l'espace hyperbolique réel I. Transformation de Poisson et fonctions sphériques
• Semi-groupe du mouvement brownienhyperbolique
• Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one

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