On one representation of analytic functions by harmonic functions

  title={On one representation of analytic functions by harmonic functions},
  author={V. Karachik},
  journal={Siberian Advances in Mathematics},
  • V. Karachik
  • Published 2008
  • Mathematics
  • Siberian Advances in Mathematics
AbstractLet 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) = u0(x) + |x|2u1(x) + |x|4u2(x) + …, where uk(x) are functions harmonic in $$ \mathcal{D} $$. This representation is a generalization of the well-known Almansi formula. 
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