椭圆型偏微分方程组解的指数性态的Agmon型估计及其在Schrödinger，Moisil-Theodorescu和Dirac算子中的应用
Agmon's type estimates of exponential behavior of solutions of systems of elliptic partial differential equations.Applications to Schrödinger, Moisil-Theodorescu and Dirac operators
摘要：
本文的目的是在$\sR^n$上得到椭圆型偏微分方程组解的Agmon型指数估计。我们发现，这些估计与一个家庭的相关的微分算子依赖于原操作员的本质谱，并与指数权重描述的解决方案在无穷大的减少。所涉及的算子的本质谱是通过其极限算子来描述的。所得结果被应用于研究矩阵薛定谔，Moisil-Theodorescu和Dirac算子的本征函数的指数衰减问题。
英文摘要：
The aim of this paper is to derive Agmon's type exponential estimates for solutions of elliptic systems of partial differential equations on $\sR^n$. We show that these estimates are related with the essential spectra of a family of associated differential operators which depend on the original operator, and with exponential weights which describe the decrease of solutions at infinity. The essential spectra of the involved operators are described by means of their limit operators. The obtained results are applied to study the problem of exponential decay of eigenfunctions of matrix Schrödinger, Moisil-Theodorescu, and Dirac operators.
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