A Two-Spheres Problem on Homogeneous Trees

m

, n two relatively prime natural numbers, if a complex valued function f on a homogeneous tree satisfies the mean value property for all spheres of radius m and all spheres of radius n, then f is harmonic.

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Received: November 27, 1995/Revised: Revised March 16, 1998

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Vieli, F. A Two-Spheres Problem on Homogeneous Trees. Combinatorica 18, 185–189 (1998). https://doi.org/10.1007/PL00009815

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  • AMS Subject Classification (1991) Classes:  05C05, 43A85