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arXiv · 2209.12211

Sharp Gaussian upper bounds for Schr\"odinger semigroups on the half-line

Paul Holst·Hendrik Vogt
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Abstract

In 1998, V. Liskevich and Y. Semenov showed sharp Gaussian upper bounds for Schr\"odinger semigroups on $\mathbb R^3$ 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.

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Paul Holst, Hendrik Vogt. 2022-09-25. Sharp Gaussian upper bounds for Schr\"odinger semigroups on the half-line. https://doi.org/10.1007/s11117-024-01087-8

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