David Borthwick

Spectral Theory of Infinite-Area Hyperbolic Surfaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book introduces geometric spectral theory in the context of Riemann surfaces. A comprehensive account is given of dramatic recent developments in the context of infinite-area hyperbolic surfaces. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, spectral theory, and ergodic theory. The book highlights these connections, at a level accessible to graduate students and researchers from a wide range of fields.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 355
• Erscheinungstermin: 13. September 2007
• Englisch
• ISBN-13: 9780817646530
• Artikelnr.: 37364227

Autorenporträt

David Borthwick is Professor and Director of the Graduate Studies Department of Mathematics and Computer Science at Emory University, Georgia, USA.

Inhaltsangabe

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.

Rezensionen

"The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)