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Spectral Theory of Infinite-Area Hyperbolic Surfaces
This book introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of dramatic recent developments in the field. These developments were prompted by advances in geometric scattering theory in the early 1990s which provided new tools for...
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| Auteur principal : | |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Spectral Theory of Infinite-Area Hyperbolic Surfaces / David Borthwick. |
| Édition : | 1st ed. 2007. |
| Publié : |
Boston, MA :
Birkhäuser Boston
, [20..] Cham : Springer Nature |
| Collection : | Progress in mathematics (Boston, Mass. Online) ; 256 |
| Accès en ligne : |
Accès Nantes Université
Accès direct soit depuis les campus via le réseau ou le wifi eduroam soit à distance avec un compte @etu.univ-nantes.fr ou @univ-nantes.fr |
| Note sur l'URL : | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex |
| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | Hyperbolic Surfaces. Compact and Finite-Area Surfaces. Spectral Theory for the Hyperbolic Plane. Model Resolvents for Cylinders. TheResolvent. Spectral and Scattering Theory. Resonances and Scattering Poles. Upper Bound for Resonances. Selberg Zeta Function. Wave Trace and Poisson Formula. Resonance Asymptotics. Inverse Spectral Geometry. Patterson Sullivan Theory. Dynamical Approach to the Zeta Function. |
| Sujets : | |
| Documents associés : | Autre format:
Spectral theory of infinite-area hyperbolic surfaces |
| Résumé : | This book introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of dramatic recent developments in the field. These developments were prompted by advances in geometric scattering theory in the early 1990s which provided new tools for the study of resonances. Hyperbolic surfaces provide an ideal context in which to introduce these new ideas, with technical difficulties kept to a minimum. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, spectral theory, and ergodic theory. The book highlights these connections, at a level accessible to graduate students and researchers from a wide range of fields. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, characterization of the spectrum, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. |
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| Notes : | L'impression du document génère 354 p. |
| Bibliographie : | Bibliogr. Index |
| ISBN : | 978-0-8176-4653-0 |
| DOI : | 10.1007/978-0-8176-4653-0 |