加权扭球平均的内射集及支撑定理
Sets of injectivity for weighted twisted spherical means and support theorems
摘要：
在这篇文章中，我们证明了球$S_R(o)=\{z\in\mathbb C^n: |z|=R\}$是集的加权扭曲球平均（WTSM）的一个合适的功能类$\mathbb C^n$。这里的权是$S^{2n-1}.$上的球谐函数。一般来说，具有实解析权的扭曲球平均（TSM）的内射集问题仍然是一个未解决的问题。我们想参考\cite{NRR}，一些结果集的内射的球形平均与真正的分析权重在欧几里德设置。
英文摘要：
In this article, we show that the spheres $S_R(o)=\{z\in\mathbb C^n: |z|=R\}$ are sets of injectivity for the weighted twisted spherical means (WTSM) for a suitable class of functions on $\mathbb C^n$. The weights here are spherical harmonics on $S^{2n-1}.$ In general, the question of set of injectivity for the twisted spherical means (TSM) with real analytic weight is still open. We would like to refer to \cite{NRR}, for some results on the sets of injectivity for the spherical means with real analytic weights in the Euclidean setup.
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