Spectral And Scattering Theory

Authors: Borthwick, David
Provides an accessible introduction to geometric scattering theory and the theory of resonances
Discusses important developments such as resonance counting, analysis of the Selberg zeta function, and the Poisson formula
New chapters cover resolvent estimates, wave propagation, and Naud’s proof of a spectral gap for convex hyperbolic surfaces
Makes use of new techniques for resonance plotting that more clearly illustrate existing results of resonance distribution

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 setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added.