Locally symmetric spaces and transfer operators

局部对称空间和传输算子

• 批准号: 264148330
• 负责人: Professorin Dr. Anke Pohl
• 金额: --
• 依托单位: Arbeitsgruppe Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/264148330?language=en
• 关键词: Locally; symmetric; spaces; transfer; operators

Over the last few decades, mathematical quantum chaos on Riemannian manifolds has been studied using an ever increasing number of methods which focus on the dynamics of the manifolds rather than on their (static) geometry. Among these dynamical methods are transfer operator techniques whose potential is still far from being fully understood.The PI has advanced significantly the development of transfer operator techniques for Riemannian hyperbolic surfaces. For a wide range of noncompact surfaces they now provide, e.g., a purely dynamical characterization of Maass cusp forms, and hence show a deeper relation between these Laplace eigenfunctions and periodic geodesics than could be established by any other method. The main theme of this project is to use the insights gained to far to further extend the investigations for hyperbolic surfaces (in particular, to resonances, non-unitary twists, etc.), and to develop transfer operator methods for higher-dimensional hyperbolic spaces and also for some higher rank Riemannian locally symmetric spaces.

在过去的几十年里，黎曼流形上的数学量子混沌已经使用越来越多的方法进行了研究，这些方法专注于流形的动力学而不是它们的（静态）几何。在这些动力学方法中，传递算子技术的潜力还远未被完全理解，PI极大地促进了黎曼双曲曲面传递算子技术的发展。对于广泛的非致密表面，它们现在提供，例如，一个纯粹的动力学表征的马斯尖点形式，因此显示了更深的关系，这些拉普拉斯特征函数和周期测地线比可以建立任何其他方法。 该项目的主题是利用迄今为止获得的见解，进一步扩展双曲曲面的研究（特别是共振，非幺正扭曲等），并发展了高维双曲空间和某些高阶黎曼局部对称空间的转移算子方法。

项目成果

Eisenstein series twisted with non-expanding cusp monodromies

爱森斯坦系列扭曲非扩展尖点单峰

• DOI: 10.1007/s11139-019-00205-5
• 发表时间: 2020
• 期刊: The Ramanujan Journal
• 作者: Anke D. Pohl;K. Fedosova
• 通讯作者: K. Fedosova

A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions

拉普拉斯本征函数和 Selberg zeta 函数零点之间基于传递算子的关系

• DOI: 10.1017/etds.2018.51
• 发表时间: 2020
• 期刊: Ergodic Theory and Dynamical Systems
• 影响因子: 0.9
• 作者: Anke D. Pohl;A. Adam
• 通讯作者: A. Adam

Fractal Weyl bounds and Hecke triangle groups

分形 Weyl 界限和 Hecke 三角形群

• DOI: 10.3934/era.2019.26.003
• 发表时间: 2019
• 期刊: Electronic Research Announcements
• 作者: Anke D. Pohl;F. Naud;L. Soares
• 通讯作者: L. Soares

Density of resonances for covers of Schottky surfaces

肖特基表面覆盖层的共振密度

• DOI: 10.4171/jst/321
• 发表时间: 2020
• 期刊: Journal of Spectral Theory
• 影响因子: 1
• 作者: Anke D. Pohl;L. Soares
• 通讯作者: L. Soares

Numerical resonances for Schottky surfaces via Lagrange–Chebyshev approximation

通过拉格朗日切比雪夫近似计算肖特基表面的数值共振

• DOI: 10.1142/s0219493721400050
• 期刊: arXiv: Spectral Theory
• 作者: Anke D. Pohl;O. Bandtlow;T. Schick;A. Weiße
• 通讯作者: A. Weiße