Functions possessing restricted mean value properties
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- by David Heath PDF
- Proc. Amer. Math. Soc. 41 (1973), 588-595 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 588-595
- MSC: Primary 31B05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0333213-1
- MathSciNet review: 0333213