$n$维实双曲空间中环形区域的球形平均值
Spherical means in annular regions in the $n$-dimensional real hyperbolic spaces
摘要：
设$Z_{r,R}$是实双曲空间$\mathbb B^n$中具有球面平均$M_sf(x)=0$的环$\Ann(r,R)$上的所有连续函数$f$的类，只要$s>0$和$x\in \mathbb B^n$使得球面$S_s(x)\subset \Ann(r, R) $和$B_r(o)\subseteq B_s(x).$.本文给出了$Z_{r,R}$中函数的一个特征.在$R=\infty$情形下，这一结果给出了实双曲空间中球平均的Helgason支撑定理的一个新的证明.
英文摘要：
Let $Z_{r,R}$ be the class of all continuous functions $f$ on the annulus $\Ann(r,R)$ in the real hyperbolic space $\mathbb B^n$ with spherical means $M_sf(x)=0$, whenever $s>0$ and $x\in \mathbb B^n$ are such that the sphere $S_s(x)\subset \Ann(r, R) $ and $B_r(o)\subseteq B_s(x).$ In this article, we give a characterization for functions in $Z_{r,R}$. In the case $R=\infty$, this result gives a new proof of Helgason's support theorem for spherical means in the real hyperbolic spaces.
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