Moment versions of the Morera problem in Cⁿ and Hⁿ

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• 作者：Berenstein ; Carlos ; Chang ; Der-Chen ; Eby ; Wayne ; Zalcman ; Lawrence
• 关键词：Heisenberg group ; Laguerre calculus ; Morera problem ; Pompeiu problem ; Moment conditions ; CR functions
• 刊名：Advances in Applied Mathematics
• 出版年：2003
• 出版时间：August, 2003
• 年：2003
• 卷：31
• 期：2
• 页码：273-300
• 全文大小：217 K

文摘

Our aim in this paper is to demonstrate how a result of [Agranovsky et al., J. Analyse Math. 57 (1992) 281–296] on Hⁿ can be extended to use more general integral conditions. In particular, we show that the conclusions of [Agranovsky et al., J. Analyse Math. 57 (1992) 281–296] 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 two spheres with the possibility of using two moments on a single sphere without any stipulation on the radius. As a precursor to investigating moments on Hⁿ, we consider how this result extends to Cⁿ.