Operator kernel estimates for functions of generalized Schrödinger operators
Operator kernel estimates for functions of generalized Schrödinger operators
复制标题
广义薛定谔算子函数的算子核估计
DOI：
10.1090/s0002-9939-02-06578-4
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发表时间：
2002
影响因子：
0.4
通讯作者：
A. Klein
中科院分区：
文献类型：
--
作者：
F. Germinet;A. Klein
本文研究了广义薛定谔算子(广义薛定谔算子是数学物理中一类半有界二阶偏微分算子，包括薛定谔算子、磁性薛定谔算子和经典波算子（即声学算子、麦克斯韦算子和其他与经典波方程相关的二阶偏微分算子）函数的算子核在远距离上的衰减。我们推导了一个改进的Combes-Thomas估计，得到了解的算子核的指数衰减率的显式下界。我们证明了对于缓慢递减的光滑函数，算子核的衰减速度比多项式快。
We study the decay at large distances of operator kernels of functions of generalized Schrodinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrodinger operator, the magnetic Schrodinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than ally polynomial.