Resolvent bounds for jump generators and ground state asymptotics for nonlocal Schr\"{o}dinger operators
Mathematical Physics
2016-06-13 v1 Functional Analysis
math.MP
Abstract
The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially we prove a number of lower and upper bounds for the resolvent of such operators. We consider two applications of these results. First we obtain pointwise estimates for principal eigenfunction of jump generators perturbed by a compactly supported potential (so-called nonlocal Schr\"odinger operators). Then we consider the Cauchy problem for the corresponding inhomogeneous evolution equations and study the behaviour of its solutions.
Keywords
Cite
@article{arxiv.1606.03381,
title = {Resolvent bounds for jump generators and ground state asymptotics for nonlocal Schr\"{o}dinger operators},
author = {Yuri Kondratiev and Stanislav Molchanov and Andrey Piatnitski and Elena Zhizhina},
journal= {arXiv preprint arXiv:1606.03381},
year = {2016}
}