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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Restricted mean values and harmonic functions


Author: John R. Baxter
Journal: Trans. Amer. Math. Soc. 167 (1972), 451-463
MSC: Primary 31B05
MathSciNet review: 0293112
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Abstract: A function h defined on a region R in $ {{\mathbf{R}}^n}$ will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0293112-4
Keywords: Harmonic, mean value, positive $ {\mathcal{L}_1}$-operator, dissipative, limit at boundary
Article copyright: © Copyright 1972 American Mathematical Society