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Pizzetti, P. (1909) Sulla media dei valori che una funzione dei punti dello spazio assume sulla superficie della sfera. Rendiconti Linzei—Matematica e Applicazioni, 18, 182-185.

has been cited by the following article:

• TITLE: Mean-Value Theorems for Harmonic Functions on the Cube in Rn

  AUTHORS: Petar Petrov

  KEYWORDS: Harmonic Functions, Polyharmonic Functions, Hypercube, Quadrature Domain, Best One-Sided Approximation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.11, September 16, 2015

  ABSTRACT: Let be a hypercube in Rn. We prove theorems concerning mean-values of harmonic and polyharmonic functions on In(r), which can be considered as natural analogues of the famous Gauss surface and volume mean-value formulas for harmonic functions on the ball in and their extensions for polyharmonic functions. We also discuss an application of these formulas—the problem of best canonical one-sided L1-approximation by harmonic functions on In(r).