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Goldstein, M., Haussmann, W. and Rogge, L. (1988) On the Mean Value Property of Harmonic Functions and Best Harmonic L1-Approximation. Transactions of the American Mathematical Society, 305, 505-515.

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).