论文标题
通过非进攻重排，拉格朗日放松和扰动，将频谱离散到Schrödinger运营商的条件
Conditions for discreteness of the spectrum to Schrödinger operator via non-increasing rearrangement, Lagrangian relaxation and perturbations
论文作者
论文摘要
这项工作是我们的Previos论文的延续，其中对于Schrödinger$ h =-Δ+ V（\ e）\ CDOT $ $（v（v（\ e）\ ge 0）$，在太空中作用于$ l_2（\ r^d）\，（\ r^d）\，（d \ ge 3）$，有足够的条件，有足够的条件，以确定其spectrum and shore shore shore shere nos a的基础 - 设置功能的优化问题，这是二进制线性编程问题的无限维度概括。根据潜在的$ V（\ e）$的非进攻重排，为频谱的离散性提供了足够的条件。使用拉格朗日放松方法来解决此优化问题，我们获得了足够的条件，可以在预期和电位偏差方面获得频谱的离散性。通过对电势的合适扰动，我们获得了频谱离散性的条件，涵盖了仅在立方体的子集上无穷大的电势，而在立方体到达无限时，其Lebesgue措施往往为零。同样，在空间$ l_2（ω）$中定义运算符$ h $的情况（$ω$是$ \ r^d $中的一个开放域）。
This work is a continuation of our previos paper, where for the Schrödinger operator $H=-Δ+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space $L_2(\R^d)\,(d\ge 3)$, some sufficient conditions for discreteness of its spectrum have been obtained on the base of well known Mazya -Shubin criterion and an optimization problem for a set function, which is an infinite-dimensional generalization of a binary linear programming problem. A sufficient condition for discreteness of the spectrum is formulated in terms of the non-increasing rearrangement of the potential $V(\e)$. Using the method of Lagrangian relaxation for this optimization problem, we obtain a sufficient condition for discreteness of the spectrum in terms of expectation and deviation of the potential. By means of suitable perturbations of the potential we obtain conditions for discreteness of the spectrum, covering potentials which tend to infinity only on subsets of cubes, whose Lebesgue measures tend to zero when the cubes go to infinity. Also the case where the operator $H$ is defined in the space $L_2(Ω)$ is considered ($Ω$ is an open domain in $\R^d$).
