On one representation of analytic functions by harmonic functions

Abstract

Let u(x) be a function analytic in some neighborhood D about the origin, D ⊂ ℝn. We study the representation of this function in the form of a series u(x) = u0(x) + x 2 u1(x) + x 4 u2(x) + x , where uk(x) are functions harmonic in D. This representation is a generalization of the well-known Almansi formula. © Allerton Press, Inc. 2008.