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Computation of eigenvalues, spectral zeta functions and zeta-determinants on hyperbolic surfaces. (English) Zbl 1390.35198

Girouard, Alexandre (ed.) et al., Geometric and computational spectral theory. Lectures from the Séminaire de Mathématiques Supérieures, Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada, June 15–26, 2015. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-2665-1/pbk; 978-1-4704-4258-3/ebook). Contemporary Mathematics 700. Centre de Recherches Mathématiques Proceedings, 177-205 (2017).
Summary: These are lecture notes from a series of three lectures given at the summer school “Geometric and Computational Spectral Theory” in Montreal in June 2015. The aim of the lecture was to explain the mathematical theory behind computations of eigenvalues and spectral determinants in geometrically non-trivial contexts.
For the entire collection see [Zbl 1377.35004].

MSC:

35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35P15 Estimates of eigenvalues in context of PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs

Software:

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References:

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