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|a 9780817646530
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|a Borthwick, David
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| 245 |
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|a Spectral Theory of Infinite-Area Hyperbolic Surfaces
|h Elektronische Ressource
|c by David Borthwick
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| 250 |
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|a 1st ed. 2007
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| 260 |
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|a Boston, MA
|b Birkhäuser
|c 2007, 2007
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| 300 |
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|a XI, 355 p
|b online resource
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| 505 |
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|a Hyperbolic Surfaces -- Compact and Finite-Area Surfaces -- Spectral Theory for the Hyperbolic Plane -- Model Resolvents for Cylinders -- TheResolvent -- Spectral and Scattering Theory -- Resonances and Scattering Poles -- Upper Bound for Resonances -- Selberg Zeta Function -- Wave Trace and Poisson Formula -- Resonance Asymptotics -- Inverse Spectral Geometry -- Patterson–Sullivan Theory -- Dynamical Approach to the Zeta Function
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| 653 |
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|a Functional analysis
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Functions of complex variables
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Functions of a Complex Variable
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Differential Geometry
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| 653 |
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|a Differential Equations
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| 653 |
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|a Differential equations
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| 653 |
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|a Mathematical Methods in Physics
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Progress in Mathematics
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| 028 |
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|a 10.1007/978-0-8176-4653-0
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| 856 |
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|u https://doi.org/10.1007/978-0-8176-4653-0?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.7
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| 520 |
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|a 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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