Moment versions of the Morera problem in Cn and Hn

Carlos Berenstein; Der Chen Chang; Wayne Eby; Lawrence Zalcman

doi:10.1016/S0196-8858(03)00092-7

Moment versions of the Morera problem in Cⁿ and Hⁿ

Carlos Berenstein, Der Chen Chang, Wayne Eby, Lawrence Zalcman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	273-300
Number of pages	28
Journal	Advances in Applied Mathematics
Volume	31
Issue number	2
DOIs	https://doi.org/10.1016/S0196-8858(03)00092-7
State	Published - Aug 2003

Bibliographical note

Funding Information:
✩ Research partially supported by NSF Grant DMS0070044, by a William Fulbright Research Grant and by GIF Grant No. G-643-117.6/1999. * Corresponding author. E-mail addresses: [email protected] (C. Berenstein), [email protected] (D.-C. Chang), [email protected] (W. Eby), [email protected] (L. Zalcman).

Funding

✩ Research partially supported by NSF Grant DMS0070044, by a William Fulbright Research Grant and by GIF Grant No. G-643-117.6/1999. * Corresponding author. E-mail addresses: [email protected] (C. Berenstein), [email protected] (D.-C. Chang), [email protected] (W. Eby), [email protected] (L. Zalcman).

Funders	Funder number
National Science Foundation	DMS0070044
Directorate for Mathematical and Physical Sciences	0070044
German-Israeli Foundation for Scientific Research and Development

Keywords

CR functions
Heisenberg group
Laguerre calculus
Moment conditions
Morera problem
Pompeiu problem

Access to Document

10.1016/S0196-8858(03)00092-7

Cite this

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title = "Moment versions of the Morera problem in Cn and Hn",

abstract = "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 zm 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.",

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author = "Carlos Berenstein and Chang, {Der Chen} and Wayne Eby and Lawrence Zalcman",

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AU - Zalcman, Lawrence

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