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- W2999685049 abstract "We give a characterization of harmonic functions by a mean value type property at a single point. We show that if u is real analytic in $$Omega ,$$ $${mathbf {a}}$$ is a fixed point of $$Omega ,$$ and if for all homogeneous polynomials p of degree k the one dimensional function $$begin{aligned} varphi _{p}left( rright) =int _{mathbb {S}}uleft( mathbf {a+} romega right) pleft( omega right) ,mathrm {d} omega, end{aligned}$$is a polynomial of degree k at the most in some interval $$0le r<eta _{p},$$ then u is harmonic in $$Omega .$$ If u is smooth, and $$eta _{p}=eta $$ does not depend on p, then we show that u must be harmonic in the ball of center $${mathbf {a}}$$ and radius $$eta .$$ We also give a result that applies to distributions. Furthermore, we characterize harmonic functions by flow integrals around a single point." @default.
- W2999685049 created "2020-01-23" @default.
- W2999685049 creator A5008853427 @default.
- W2999685049 date "2020-01-13" @default.
- W2999685049 modified "2023-10-16" @default.
- W2999685049 title "Characterization of harmonic functions by the behavior of means at a single point" @default.
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- W2999685049 doi "https://doi.org/10.1007/s42985-019-0003-z" @default.
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