English

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 R3\mathbb R^3 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

R2 v1 2026-06-28T02:02:47.433Z