Spectral Theory of Infinite-Area Hyperbolic Surfaces

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Borthwick, David (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2007.
Edición:1st ed. 2007.
Colección:Progress in Mathematics, 256
Temas:
Functional analysis.
Differential equations.
Functions of complex variables.
Geometry, Differential.
Mathematical physics.
Functional Analysis.
Differential Equations.
Functions of a Complex Variable.
Differential Geometry.
Mathematical Methods in Physics.
Acceso en línea:Texto Completo
Descripción
Sumario: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.
Descripción Física:XI, 355 p. online resource.
ISBN:9780817646530
ISSN:2296-505X ;

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