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

 

Functions possessing restricted mean value properties


Author: David Heath
Journal: Proc. Amer. Math. Soc. 41 (1973), 588-595
MSC: Primary 31B05
MathSciNet review: 0333213
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Abstract: A real-valued function $ f$ defined on an open subset of $ {R^N}$ is said to have the restricted mean value property with respect to balls (spheres) if, for each point $ x$ in the set, there exists a ball (sphere) with center $ x$ and radius $ r(x)$ such that the average value of $ f$ over the ball (sphere) is equal to $ f(x)$. If $ f$ is harmonic then it has the restricted mean value property. Here new conditions for the converse implication are given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0333213-1
PII: S 0002-9939(1973)0333213-1
Keywords: Harmonic function, mean value property, Markov process
Article copyright: © Copyright 1973 American Mathematical Society