Moment versions of the Morera problem in \(\mathbb C^n\) and \(\mathbb H^n\). (Q1415378)

From authors' abstract: The aim of this paper is to show that a result of \textit{M. Agranovsky} et al. [J. Anal. Math. 57, 282--296 (1991; Zbl 0773.32012)] on \(\mathbb H^n\) can be extended to use more general integral conditions. In particular, it is shown that their conclusions remain valid when a weight \(z^m\) is included in the integral conditions. This question relates to a result of Zalcman for Euclidean space, which replaces a requirement for 2 spheres with the possibility of using 2 moments on a single sphere without any stipulation on the radius. As a precursor to investigating moments on \(\mathbb H^n\), the authors consider how this result extends to \(\mathbb C^n\).