We establish a criterion of extendability of a function harmonic in a ball of the n-dimensional space to an entire harmonic function and study the growth of an entire harmonic function in terms of the best approximation of this function by harmonic polynomials.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 4, pp. 464–470, April, 2018.
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Veselovs’ka, O.V. On the Approximation and Growth of Entire Harmonic Functions in ℝn. Ukr Math J 70, 532–539 (2018). https://doi.org/10.1007/s11253-018-1514-z
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DOI: https://doi.org/10.1007/s11253-018-1514-z