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On one representation of analytic functions by harmonic functions

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Abstract

Let u(x) be a function analytic in some neighborhood D about the origin, \( \mathcal{D} \) ⊂ ℝn. We study the representation of this function in the form of a series u(x) = u 0(x) + |x|2 u 1(x) + |x|4 u 2(x) + …, where u k (x) are functions harmonic in \( \mathcal{D} \). This representation is a generalization of the well-known Almansi formula.

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Authors and Affiliations

  1. Southern-Ural State University, Chelyabinsk, 454080, Russia

    V. V. Karachik

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  1. V. V. Karachik
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Correspondence to V. V. Karachik.

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Original Russian Text © V. V. Karachik, 2007, published in Matematicheskie Trudy, 2007, Vol. 10, No. 2, pp. 142–162.

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Karachik, V.V. On one representation of analytic functions by harmonic functions. Sib. Adv. Math. 18, 103–117 (2008). https://doi.org/10.3103/S1055134408020041

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  • DOI: https://doi.org/10.3103/S1055134408020041

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