Almost periodic and related multi-dimensional spectral problems

我们计划研究在多维空间中作用的具有近周期系数的算子。从物理角度来看，这样的算子是非常有趣的。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所知甚少。我们计划开发一种新的方法来处理这些算子，称为多尺度变分方法。我们还计划研究一些其他问题，我们认为这些问题的风险比主要问题低。

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.