Spectral Theory of Infinite-Area Hyperbolic Surfaces

• Main Author: Borthwick, David (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2007.
• Series: Progress in Mathematics ; 256
• Subjects: Mathematics.; Functional analysis.; Functions of complex variables.; Partial differential equations.; Differential geometry.; Physics.; Functional Analysis.; Partial Differential Equations.; Functions of a Complex Variable.; Differential Geometry.; Mathematical Methods in Physics.

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...

Table of Contents:

• 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.