Titlebook: Spectral Theory of Infinite-Area Hyperbolic Surfaces; David Borthwick Book 2016Latest edition Springer International Publishing Switzerlan

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Patterson-Sullivan Theory,The exponent of convergence . of a Fuchsian group . was defined in (.). We also noted some basic facts about the exponent:

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David BorthwickProvides an accessible introduction to geometric scattering theory and the theory of resonances.Discusses important developments such as resonance counting, analysis of the Selberg zeta function, and

裹住

Model Resolvents for Cylinders,ese explicit formulas will serve as building blocks when we turn to the construction of the resolvent in the general case in Chapter 6 This is because of the decomposition result of Theorem 2.23, which showed that the ends of non-elementary hyperbolic surfaces are funnels and cusps.

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Selberg Zeta Function,h spectrum of . (or, equivalently, to traces of conjugacy classes of .). We will see in this chapter that it deserves to be thought of as a spectral invariant as well, by virtue of a beautiful correspondence between resonances of . and the zeros of ..(.).

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AVERT

Inverse Spectral Geometry,em is to deduce geometric properties from some knowledge of the spectrum. In the case of a surface with hyperbolic ends, the input data could include the resonance set, the scattering phase, perhaps even the scattering matrix for a particular set of frequencies.

类似思想

Numerical Computations,he Selberg zeta function has the same difficulty; the formula does not apply in the region of interest. However, for hyperbolic surfaces without cusps, the dynamical zeta function introduced in §15.3 provides a suitable alternative. The transfer operator is trace-class for any value of ., so analytic continuation is not required.

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Spectral Theory of Infinite-Area Hyperbolic Surfaces978-3-319-33877-4Series ISSN 0743-1643 Series E-ISSN 2296-505X