Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering
Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering
复制标题
有损散射中自由分解和共振的限制界
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Hart F. Smith
中科院分区：
文献类型：
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作者：
J. Galkowski;Hart F. Smith
我们建立了自由绿色函数对$\mathbb{R}^d$中超曲面的限制的高能L^2 $估计。作为一个应用，我们估计了由$V\otimes \delta_{\Gamma}$形式的势散射的对数共振自由区域的大小，其中$\Gamma \subset \mathbb{R}^d$是嵌入超曲面的紧致子集的有限并集.在奇数维中，我们证明了这样一个潜在的波动方程的解决方案的共振展开。
We establish high energy $L^2$ estimates for the restriction of the free Green's function to hypersurfaces in $\mathbb{R}^d$. As an application, we estimate the size of a logarithmic resonance free region for scattering by potentials of the form $V\otimes \delta_{\Gamma}$, where $\Gamma \subset \mathbb{R}^d$ is a finite union of compact subsets of embedded hypersurfaces. In odd dimensions we prove a resonance expansion for solutions to the wave equation with such a potential.