Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces

DOI10.1016/j.matpur.2004.01.005zbMath1072.35136OpenAlexW2078468302MaRDI QIDQ1887203

Yuzuru Inahama, Shin-Ichi Shirai

Publication date: 23 November 2004

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2004.01.005

zbMATH Keywords

hyperbolic spacespectral asymptoticsLaplaciansemiclassical result

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Cites Work

• Expansion in automorphic eigenfunctions of the Laplace-Beltrami operator in classical symmetric spaces of rank one, and the Selberg trace formula
• Positive generalized Wiener functions and potential theory over abstract Wiener spaces
• Eigenvalue asymptotics for the Schrödinger operators on the hyperbolic plane
• Quasi sure analysis of stochastic flows and Banach space valued smooth functionals on the Wiener space
• Kernels of Trace Class Operators
• Analysis on Root Systems
• Semi-groupe du mouvement brownienhyperbolique
• Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds
• 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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