Heat traces and existence of scattering resonances for bounded potentials

Heat traces and existence of scattering resonances for bounded potentials
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热迹和有界势的散射共振的存在

DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Zworski
M. Zworski
中科院分区：
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文献类型：
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作者：
Hart F. Smith;M. Zworski

文献摘要

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我们证明了，在奇数维中，紧支撑的任何实值有界势至少有一个散射共振。对于三维和更高的维度，这以前只知道足够光滑的位势。证明是基于一个逆结果，即关联热核的迹有一个适当的渐近展开当且仅当势是光滑的。
We show that, in odd dimensions, any real valued, bounded potential of compact support has at least one scattering resonance. For dimensions three and higher this was previously known only for sufficiently smooth potentials. The proof is based on an inverse result, which states that the trace of the associated heat kernel has an appropriate asymptotic expansion if and only if the potential is smooth.