Spectral Theory of Infinite-Area Hyperbolic Surfaces. 2nd ed. 2016

種類:

電子ブック

責任表示:

by David Borthwick

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016

著者名:

• Borthwick, David.
• SpringerLink (Online service)

シリーズ名:

Progress in Mathematics ; 318

ISBN:

9783319338774 [3319338773]    

注記:

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.
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, 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. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constan

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