Semiklassische Analysis mit Singularitäten

具有奇点的半经典分析

• 批准号: 5396168
• 负责人: Professor Dr. Jochen Brüning
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2004-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5396168?language=en
• 关键词: Semiklassische; Analysis; mit; Singularit; ten

In this project we are going to study the construction of semiclassical spectral asymptotics for pseudodifferential operators using singular invariant varieties of the corresponding classical Hamiltonian. For a wide class of pseudodifferential operators, we plan to study the existence of such asymptotics, the accuracy of the approximation, the relationship between semiclassical asymptotics and the topological classification of critical manifolds, and various related questions. We expect that the results will be applicable to the asymptotic description of the spectral bands in periodic and gauge-periodic problems and to finding spectral asymptotics in problems with non-integrable Hamiltonians.

在这个项目中，我们将研究伪微分算子的半经典谱渐近性的构造，利用相应的经典哈密顿量的奇异不变簇。对于广泛的一类伪微分算子，我们计划研究这种渐近性的存在性、逼近的准确性、半经典渐近性与临界流形的拓扑分类之间的关系以及各种相关问题。我们期望，结果将适用于渐近描述的谱带在周期和规范周期的问题，并找到谱渐近的问题与不可积的Hamilton。