Spectral Theory of Infinite-Area Hyperbolic Surfaces

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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• Geometria não-euclidiana
• Cálculo diferencial e equações
• Análise funcional e transforma
• Análise complexa, variáveis ??complexas
• Física Matemática

Complex Analysis;Hyperbolic Surface;Resonance Theory;Scattering Theory;Spectral Gap;Spectral Theory;partial differential equations