Finely Harmonic Functions need not be Quasi-Analytic |
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Authors: | Lyons Terry |
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Affiliation: | Department of Mathematics, Imperial College London SW7 2BZ |
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Abstract: | If a function f is harmonic on a connected open set Rd andis constant in a neighbourhood of one point in then it is identicallyconstant. We give an example of a non-constant finely harmonicfunction defined on E={zC||z|<2}p which is identically zeroon |z|1. The exceptional set P is of capacity zero so E is finelyopen and finely connected. This example therefore shows thatfinely harmonic functions are not globally determined by theirlocal behaviour. |
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