On a scattering length for additive functionals and spectrum of fractional Laplacians with non-local perturbations
On a scattering length for additive functionals and spectrum of fractional Laplacians with non-local perturbations
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关于加性泛函的散射长度和具有非局部扰动的分数拉普拉斯谱
DOI：
10.1002/mana.201800254
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发表时间：
2020
影响因子：
1
通讯作者：
Daehong Kim and Masakuni Matsuura
中科院分区：
文献类型：
--
作者：
Daehong Kim and Masakuni Matsuura
本文研究了对称稳定过程的正可加泛函的散射长度。这里考虑的加性泛函不一定是连续的。我们证明了散射长度的半经典极限等于某一测势的支撑力，从而推广了前人关于正连续可加泛函的结果。通过考虑散射长度与薛定谔算子谱底之间的关系，给出了具有测值非局部算子扰动的分数拉普拉斯算子具有关于散射长度的纯离散谱的一个等价准则。
In this paper we study the scattering length for positive additive functionals of symmetric stable processes on. The additive functionals considered here are not necessarily continuous. We prove that the semi‐classical limit of the scattering length equals the capacity of the support of a certain measure potential, thus extend previous results for the case of positive continuous additive functionals. We also give an equivalent criterion for the fractional Laplacian with a measure valued non‐local operator as a perturbation to have purely discrete spectrum in terms of the scattering length, by considering the connection between scattering length and the bottom of the spectrum of Schrödinger operator in our settings.