$C ^n$中环形区域的扭球平均及支撑定理
Twisted spherical means in annular regions in $C ^n$ and support theorems
摘要：
设$Z(Ann(r,R))$是$\mathbb C^n$中环$Ann(r,R)$上的所有连续函数$f$的类，且具有扭曲球平均$f \times μ_s(z)=0,$，只要$z\in \mathbb C^n$和$s >0$满足球$S_s(z)\subseteq Ann(r, R) $和球$B_r(0)\subseteq B_s(z).$的条件本文给出了$Z(Ann(r,R))$中函数的球调和系数的一个刻划.我们还证明了支持定理的扭曲球形手段在$\mathbb C^n$，改善了一些早期的结果。
英文摘要：
Let $Z(Ann(r,R))$ be the class of all continuous functions $f$ on the annulus $Ann(r,R)$ in $\mathbb C^n$ with twisted spherical mean $f \times μ_s(z)=0,$ whenever $z\in \mathbb C^n$ and $s >0$ satisfy the condition that the sphere $S_s(z)\subseteq Ann(r, R) $ and ball $B_r(0)\subseteq B_s(z).$ In this paper, we give a characterization for functions in $Z(Ann(r,R))$ in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in $\mathbb C^n$ which improve some of the earlier results.
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