Localization and Schr\"odinger perturbations of kernels

TL;DR

This paper investigates the behavior of integral kernels under Schr"odinger perturbations, providing exponential estimates and extending classical inequalities to a broader class of kernels, including Markovian semigroups.

Contribution

It introduces new exponential estimates for Schr"odinger perturbations of integral kernels satisfying transience conditions, generalizing Gronwall's inequality.

Findings

Established exponential bounds for kernel iterations.

Extended estimates to Schr"odinger perturbations of Markovian semigroups.

Provided a framework for analyzing kernel perturbations under transience conditions.

Abstract

We study iterations of integral kernels satisfying a transience-type condition and we prove exponential estimates analogous to Gronwall\rq{}s inequality. As a consequence we obtain estimates of Schr\"odinger perturbations of integral kernels, including Markovian semigroups.