Sharp Gaussian upper bounds for Schr\"odinger semigroups on the half-line
Functional Analysis
2024-11-13 v3 Analysis of PDEs
Abstract
In 1998, V. Liskevich and Y. Semenov showed sharp Gaussian upper bounds for Schr\"odinger semigroups on with potentials satisfying a global Kato class condition. Using similar basic ideas we show sharp Gaussian upper bounds for Schr\"odinger semigroups on the half-line, also assuming a suitable global Kato class condition. Our proof strategy includes a new technique of weighted ultracontractivity estimates.
Cite
@article{arxiv.2209.12211,
title = {Sharp Gaussian upper bounds for Schr\"odinger semigroups on the half-line},
author = {Paul Holst and Hendrik Vogt},
journal= {arXiv preprint arXiv:2209.12211},
year = {2024}
}
Comments
updated, with more explanations, some errors corrected