Regularized Trace of the Perturbed Laplace--Beltrami Operator on Two-Dimensional Manifolds with Closed Geodesics

T. V. Zykova

Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 373-389.

Résumé

The main result of the paper is the determination of the regularized trace of the Laplace–Beltrami operator with potential on the manifold given by a function family of smooth almost Liouville metrics on the sphere (besides, all the geodesics of these metrics are closed and have equal length).

Détail

Keywords: Laplace–Beltrami operator, almost Liouville metric, two-dimensional manifold, geodesic, sphero-conical coordinates, metric, pseudodifferential operator, bundle of half-densities, Hamiltonian flow, Dirichlet series
Mots-clés : cotangent space.

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