Spectral Theory of Infinite-Area Hyperbolic Surfaces

• Κύριος συγγραφέας: Borthwick, David (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Έκδοση: 2nd ed. 2016.
• Σειρά: Progress in Mathematics, 318
• Θέματα: Mathematics.; Functional analysis.; Functions of complex variables.; Partial differential equations.; Hyperbolic geometry.; Physics.; Functional Analysis.; Partial Differential Equations.; Functions of a Complex Variable.; Hyperbolic Geometry.; Mathematical Methods in Physics.

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...

Πίνακας περιεχομένων:

• 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.