Mean-value characterization of pluriharmonic and separately harmonic functions

L. A. Aizenberg; C. A. Berenstein; L. Wertheim

doi:10.2140/pjm.1996.175.295

Mean-value characterization of pluriharmonic and separately harmonic functions

L. A. Aizenberg
, C. A. Berenstein
, L. Wertheim

University of Maryland, College Park

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

3 Scopus citations

Abstract

We show that separately harmonic functions and pluriharmonic functions in Cⁿ can be characterized by a finite number of mean-value conditions over boundaries of ellipsoids or distinguished boundaries of polydisks. This is a generalization of the Delsarte-Lions characterization of harmonic functions and of the Morera theorem for holomorphic functions.

Original language	English
Pages (from-to)	295-306
Number of pages	12
Journal	Pacific Journal of Mathematics
Volume	175
Issue number	2
DOIs	https://doi.org/10.2140/pjm.1996.175.295
State	Published - Oct 1996
Externally published	Yes

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title = "Mean-value characterization of pluriharmonic and separately harmonic functions",

abstract = "We show that separately harmonic functions and pluriharmonic functions in Cn can be characterized by a finite number of mean-value conditions over boundaries of ellipsoids or distinguished boundaries of polydisks. This is a generalization of the Delsarte-Lions characterization of harmonic functions and of the Morera theorem for holomorphic functions.",

author = "Aizenberg, \{L. A.\} and Berenstein, \{C. A.\} and L. Wertheim",

year = "1996",

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doi = "10.2140/pjm.1996.175.295",

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AU - Aizenberg, L. A.

AU - Berenstein, C. A.

AU - Wertheim, L.

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N2 - We show that separately harmonic functions and pluriharmonic functions in Cn can be characterized by a finite number of mean-value conditions over boundaries of ellipsoids or distinguished boundaries of polydisks. This is a generalization of the Delsarte-Lions characterization of harmonic functions and of the Morera theorem for holomorphic functions.

AB - We show that separately harmonic functions and pluriharmonic functions in Cn can be characterized by a finite number of mean-value conditions over boundaries of ellipsoids or distinguished boundaries of polydisks. This is a generalization of the Delsarte-Lions characterization of harmonic functions and of the Morera theorem for holomorphic functions.

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EP - 306

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Mean-value characterization of pluriharmonic and separately harmonic functions

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