| 书目名称 | Spectral Theory of Infinite-Area Hyperbolic Surfaces | | 编辑 | David Borthwick | | 视频video | http://file.papertrans.cn/874/873879/873879.mp4 | | 概述 | Provides 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 | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | .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 constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance | | 出版日期 | Book 2016Latest edition | | 关键词 | Complex Analysis; Hyperbolic Surface; Resonance Theory; Scattering Theory; Spectral Gap; Spectral Theory; | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-319-33877-4 | | isbn_softcover | 978-3-319-81622-7 | | isbn_ebook | 978-3-319-33877-4Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer International Publishing Switzerland 2016 |
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