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arXiv · 2104.00833

On the trace of the wave group and regularity of potentials

Hart F. Smith
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Abstract

For the wave equation $\partial_t^2-\Delta+V$ on $\mathbb{R}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\rightarrow 0$ for the relative trace of the wave group.

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Hart F. Smith. 2021-04-02. On the trace of the wave group and regularity of potentials. https://arxiv.org/abs/2104.00833

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