Resolvent bounds for repulsive potentials

Andr\'es Larra\'in-Hubach; Jacob Shapiro; Joseph Tiller; Yulong Li

arxiv: 2502.05614 · v2 · pith:ORRD6ASQnew · submitted 2025-02-08 · 🧮 math.AP

Resolvent bounds for repulsive potentials

Andr\'es Larra\'in-Hubach , Yulong Li , Jacob Shapiro , Joseph Tiller This is my paper

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keywords repulsiveboundspotentialresolventabsorptionapplicationassociatedcompactly

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We prove limiting absorption resolvent bounds for the semiclassical Schr\"odinger operator with a repulsive potential in dimension $n\ge 3$, which may have a singularity at the origin. As an application, we obtain time decay for the weighted energy of the solution to the associated wave equation with a short range repulsive potential and compactly supported initial data.

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