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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the mean-value property of harmonic functions


Authors: Myron Goldstein and Wellington H. Ow
Journal: Proc. Amer. Math. Soc. 29 (1971), 341-344
MSC: Primary 31.10
MathSciNet review: 0279320
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Abstract: In this note we show that if the areal mean-value theorem holds for a plane domain (subject to a mild regularity condition) for all integrable harmonic functions, then the domain must be a disk. It is also shown that if a plane domain with finite area has at least two boundary components which are continua then the mean-value property cannot hold for the class of all integrable harmonic functions with single-valued harmonic conjugates.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279320-1
PII: S 0002-9939(1971)0279320-1
Keywords: Kernel function, mean-value property, principal function, normal operator, boundary component
Article copyright: © Copyright 1971 American Mathematical Society