论文标题
广义Schrödinger系统基本矩阵的指数衰减估计值
Exponential Decay Estimates for Fundamental Matrices of Generalized Schrödinger Systems
论文作者
论文摘要
在本文中，我们研究了广义Schrödinger运营商及其基本矩阵的系统。更具体地说，我们确定了这种基本矩阵的存在，然后证明了它们的上下指数衰减的敏锐型号估计值。我们认为的Schrödinger运算符具有领先的系数，这些系数是有界和椭圆形的，而零阶项被认为是非排定的，并且属于反向Hölder矩阵类别。特别是，我们的操作员不必是自我伴侣。指数边界受所谓的与反向Hölder矩阵相关的所谓上下AGMON距离，该距离用作潜在函数。此外，我们彻底讨论了这种新的反向Hölder矩阵类，更古典的矩阵$ \ MATHCAL {a} _ {p，\ infty} $ class和矩阵$ \ mathcal {a} _} _ {_ {\ infty} $ class在[dall15中引入[dall15]。
In this article, we investigate systems of generalized Schrödinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay estimates for them. The Schrödinger operators that we consider have leading coefficients that are bounded and uniformly elliptic, while the zeroth-order terms are assumed to be nondegenerate and belong to a reverse Hölder class of matrices. In particular, our operators need not be self-adjoint. The exponential bounds are governed by the so-called upper and lower Agmon distances associated to the reverse Hölder matrix that serves as the potential function. Furthermore, we thoroughly discuss the relationship between this new reverse Hölder class of matrices, the more classical matrix $\mathcal{A}_{p,\infty}$ class, and the matrix $\mathcal{A}_{\infty}$ class introduced in [Dall15].
