Advanced Search

Let $Z\left(\mathrm{Ann}\right(r,R\left)\right)$ be the class of all continuous functions $f$ on the annulus $\mathrm{Ann}(r,R)$ in ${ℂ}^n$ with twisted spherical mean $f\times {\mu }_s\left(z\right)=0,$ whenever $z\in {ℂ}^n$ and $s\>0$ satisfy the condition that the sphere $S_s\left(z\right)\subseteq \mathrm{Ann}(r,R)$ and ball $B_r\left(0\right)\subseteq B_s\left(z\right).$ In this paper, we give a characterization for functions in $Z\left(\mathrm{Ann}\right(r,R\left)\right)$ in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in ${ℂ}^n$ which improve some of the earlier results.