Almost periodic and related multi-dimensional spectral problems

几乎周期性和相关的多维谱问题

• 批准号: EP/J016829/1
• 负责人: Leonid Parnovski
• 金额: $ 56.36万
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ016829%2F1
• 关键词: Almost; periodic; related; multi; dimensional

We plan to study operators with almost-periodic coefficients acting in multidimensional spaces. Such operators are very interesting from physical point of view. They are also very interestingand challenging mathematically, since at present only very little is known about their spectra. We plan to develop a new method for working with such operators, called the milti-scale variational approach. We also plan to study a number of other problems, which we consider to be of lower risk than the main problem.

我们计划研究具有概周期系数的算子在多维空间中的作用。从物理角度来看，这样的操作员非常有趣。它们在数学上也非常有趣和具有挑战性，因为目前对它们的光谱知之甚少。我们计划开发一种处理这种算子的新方法，称为多尺度变分方法。我们还计划研究其他一些问题，我们认为这些问题的风险低于主要问题。

项目成果

On the spectrum of an "even" periodic Schroedinger operator with a rational magnetic flux

具有有理磁通量的“偶”周期薛定谔算子的谱

• DOI: 10.48550/arxiv.1308.5323
• 发表时间: 2013
• 作者: Filonov N

Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds

某些准黎曼流形上的谱分析和阿哈罗诺夫-玻姆效应

• DOI: 10.1080/03605302.2015.1095766
• 发表时间: 2015
• 期刊: Communications in Partial Differential Equations
• 影响因子: 1.9
• 作者: Boscain U

The Steklov spectrum of surfaces: asymptotics and invariants

曲面的 Steklov 谱：渐近和不变量

• DOI: 10.48550/arxiv.1311.5533
• 发表时间: 2013
• 作者: Girouard A

On the spectrum of an "even" periodic Schrödinger operator with a rational magnetic flux

具有有理磁通量的“偶”周期薛定谔算子的谱

• DOI: 10.4171/jst/102
• 发表时间: 2015
• 期刊: Journal of Spectral Theory
• 影响因子: 1
• 作者: Filonov N

Convergence of perturbation series for unbounded monotone quasiperiodic operators

• DOI: 10.1016/j.aim.2022.108647
• 发表时间: 2020-05
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: I. Kachkovskiy;L. Parnovski;R. Shterenberg