ENGLISH

Spectral Theory of Infinite-Area Hyperbolic Surfaces

By David Borthwick (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2007
ISBN
0817645241, 9780817645243, 9780817646530, 0817646531
DOI
10.1007/978-0-8176-4653-0
Open Library ID
OL11388118M
Language
english
Format
PDF
Filesize
3 MB (2827539 bytes)
Series
Progress in Mathematics 256
Edition
1
Pages
355\355
Scanned
no
Time added
2010-02-18 13:16:04
Partial Differential Equations; Functions of a Com

Description

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 the study of resonances. Hyperbolic surfaces provide an ideal context in which to introduce these new ideas, with technical difficulties kept to a minimum. 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. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, characterization of the spectrum, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function.

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