Resonances as Viscosity Limits for Exponentially Decaying Potentials

具有指数衰减相关的非单调位势随机算子的局部化

Localization for random operators with non-monotone potentials with exponentially decaying correlations

我考虑随机薛定谔算子与指数衰减的单网站的潜力，这是允许改变的迹象。对于这个模型，我证明了安德森本地化的意义下，指数衰减的本征函数和动力学本地化。此外，结果意味着Wegner型估计足够强，可以用于经典形式的多尺度分析。

一类概周期算子的指数衰减特征向量

Exponentially decaying eigenvectors for certain almost periodic operators

对于某些具有复位势的一维Schroedinger型差分算子，存在一个指数衰减的特征向量的“完备”集。“完备性”意味着所涉及的参数是通过对黎曼曲面上的解析函数求值而获得的。

From quasimodes to resonances: exponentially decaying perturbations

We consider self-adjoint operators of black-box type which are exponentially close to the free Laplacian near infinity, and prove an exponential bound for the resolvent in a strip away from resonances. Here the resonances are defined as poles of the meromorphic continuation of the resolvent between appropriate exponentially weighted spaces. We then use a local version of the maximum principle to prove that any cluster of real quasimodes generates at least as many resonances, with multiplicity, rapidly converging to the quasimodes.

Dirac operators with exponentially decaying entropy

We prove that the Weyl function of the one-dimensional Dirac operator on the half-line $\mathbb{R}_+$ with exponentially decaying entropy extends meromorphically into the horizontal strip $\{0\ge \mbox{Im}\,z > -δ\}$ for some $δ> 0$ depending on the rate of decay. If the entropy decreases very rapidly then the corresponding Weyl function turns out to be meromorphic in the whole complex plane. In this situation we show that poles of the Weyl function (scattering resonances) uniquely determine the operator.

递归系数指数衰减的正交多项式

Orthogonal polynomials with exponentially decaying recursion coefficients

我们回顾最近的结果$\mathbb{R}$和$\partial\mathbb{D}$上的措施，以产生相应的正交多项式的递归系数的指数衰减的充要条件。我们包括详细的渐进性的递归系数的详细分析的措施的关系的结果。我们提出了一个类似的Carmona的公式OPRL。Szego和Jost职能发挥了重要作用。

具有指数衰减势的一维薛定谔算子的半经典低能散射

Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials

我们考虑实直线上的半经典薛定谔算子，其形式为$$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$，其中$\hbar>0$很小。假设潜在的$V$是平滑的，积极的，并指数衰减到无穷大。我们建立了Jost解$f_\pm(\cdot,E;\hbar)$的半经典整体表示，对于小的$E$和$\hbar$，误差项是一致控制的，并构造了散射矩阵以及与$H(\hbar)$相关的半经典谱测度.这对于获得相应的波流和薛定谔流的衰减边界是至关重要的。作为一个应用程序，我们考虑的波动方程的史瓦西背景的大角动量$\ell$的小参数$\hbar$的作用是由$\ell^{-1}$。从本文和\cite{DSS2}的结果可以看出，在\cite{DSS1}，\cite{DS}中得到的各个角动量$\ell$的衰变边界可以求和，从而得到没有对称性假设的数据的急剧$t^{-3}$衰变。