Estimate of the difference between the Kac operator and the Schrödinger semigroup
Estimate of the difference between the Kac operator and the Schrödinger semigroup
复制标题
Kac 算子与薛定谔半群之间差异的估计
DOI：
10.1007/bf02885677
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发表时间：
1997
影响因子：
2.4
通讯作者：
Satoshi Takanobu
中科院分区：
文献类型：
--
作者：
T. Ichinose;Satoshi Takanobu
证明了Kac算子与Schr dinger半群之间的差的算子范数估计，并利用它给出了Schr dinger算子在L算子范数下的Trotter乘积公式的一个变形.这扩展了Helffer的结果在theL 2算子规范的情况下，在theLoperator规范更一般的标量势和矢量势。证明方法是基于Feynman-Kac和Feynman-Kac-Itô公式的概率方法。
An operator norm estimate of the difference between the Kac operator and the Schrödinger semigroup is proved and used to give a variant of the Trotter product formula for Schrödinger operators in theLpoperator norm. This extends Helffer’s result in theL2operator norm to the case in theLpoperator norm for more general scalar potentials and with vector potentials. The method of the proof is probabilistic based on the Feynman—Kac and Feynman—Kac—Itô formula.