Vol. 175, No. 2, 1996

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Mean-value characterization of pluriharmonic and separately harmonic functions

Lev Abramovich Aĭzenberg, Carlos A. Berenstein and L. Wertheim

Vol. 175 (1996), No. 2, 295–306
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.

Mathematical Subject Classification 2000
Primary: 32F05
Secondary: 31B05
Milestones
Received: 30 August 1994
Published: 1 October 1996
Authors
Lev Abramovich Aĭzenberg
Department of Mathematics and Statistics
Bar-Ilan University
52900 Ramat-Gan
Israel
http://u.cs.biu.ac.il/~aizenbrg/index.html
Carlos A. Berenstein
Mathematics and the Institute for Systems Research
University of Maryland
College Park MD 20742
United States
http://www.isr.umd.edu/~carlos/
L. Wertheim