Sets of injectivity for weighted twisted spherical means and support theorems

Abstract

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.