Spherical means in annular regions in the $n$-dimensional real hyperbolic spaces

Details Spherical means in annular regions in the $n$-dimensional real hyperbolic spaces Spherical means in annular regions in the $n$-dimensional real hyperbolic spaces

2009-08-17

arxiv.org/abs/0908.2289v5

Proc. Indian. Acad. Sci., 121 (2011), No.3, 311-325

Mathematics

Functional Analysis

published: Proc. Indian. Acad. Sci., 121 (2011), No.3, 311-325

Scientific paper

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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