Topics in Analysis on Non-Compact Manifolds

FastLane网站的DMS-0107796相关信息。主要研究者：Mikhail Shubin。摘要。它计划获得必要和充分条件，以及明确的必要和明确的充分条件，磁Schroedinger算子的谱的离散性在欧氏空间和黎曼流形的几何限制。 假定条件将以场的分离和有效势的形式给出。他们将使用维纳容量和它的推广-磁容量。物理上，我们正在寻找的条件时，电子显示一个离散的频谱，并被限制在有界域的任何固定值的能量，当这样的行为的电子的结果从电场和磁场的联合作用。

Information about DMS-0107796 for FastLane website. Principal investigator: Mikhail Shubin.Abstract.It is planned to obtain necessary and sufficient conditions, as well as explicit necessary and explicit sufficient conditions, for the discreteness of spectrum of magnetic Schroedinger operators on Euclidean space and on Riemannian manifods with geometric restrictions. Presumably the conditions will be given in terms of separation of fields and effective potentials. They will use Wiener capacity and its generalization - magnetic capacity.Physically we are looking for conditions when electrons display a discrete spectrum and are confined into bounded domains for any fixed value of their energy, when such a behavior of electrons results from a joint action of electric and magnetic fields.