Spectral Theory of Infinite-Area Hyperbolic Surfaces

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This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural set...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Borthwick, David (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
Édition:2nd ed. 2016.
Collection:Progress in Mathematics, 318
Sujets:
Functional analysis.
Differential equations.
Functions of complex variables.
Geometry, Hyperbolic.
Mathematical physics.
Functional Analysis.
Differential Equations.
Functions of a Complex Variable.
Hyperbolic Geometry.
Mathematical Methods in Physics.
Accès en ligne:Texto Completo
Table des matières:
  • Introduction
  • Hyperbolic Surfaces
  • Selberg Theory for Finite-Area Hyperbolic Surfaces
  • Spectral Theory for the Hyperbolic Plane
  • Model Resolvents for Cylinders
  • The Resolvent
  • Spectral and Scattering Theory
  • Resonances and Scattering Poles
  • Growth Estimates and Resonance Bounds
  • Selberg Zeta Function
  • Wave Trace and Poisson Formula
  • Resonance Asymptotics
  • Inverse Spectral Geometry
  • Patterson-Sullivan Theory
  • Dynamical Approach to the Zeta Function
  • Numerical Computations
  • Appendix
  • References
  • Notation Guide
  • Index.

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