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Expansion in automorphic eigenfunctions of the Laplace-Beltrami operator in classical symmetric spaces of rank one, and the Selberg trace formula

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Publication:1217956
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zbMath0306.35071MaRDI QIDQ1217956

Alexei Venkov

Publication date: 1975

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)



Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Harmonic analysis on homogeneous spaces (43A85) General theory of partial differential operators (47F05) Differential geometry of symmetric spaces (53C35) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)


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Eisenstein matrix and existence of cusp forms in rank one symmetric spaces, Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces, Sphere packing bounds via spherical codes, Large deviations for the radial processes of the Brownian motions on hyperbolic spaces, Selberg super-trace formula for super Riemann surfaces. II: Elliptic and parabolic conjugacy classes, and Selberg super-zeta functions, 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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