Sets of injectivity for weighted twisted spherical means and support theorems

Details Sets of injectivity for weighted twisted spherical means and support theorems Sets of injectivity for weighted twisted spherical means and support theorems

2010-12-23

arxiv.org/abs/1012.5167v7

Mathematics

Functional Analysis

Journal of Fourier Analysis and Applications (accepted)

Scientific paper

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 sets 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.

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