Author(s)

Petar Petrov^*

Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria.

Let be a hypercube in Rⁿ. We prove theorems concerning mean-values of harmonic and polyharmonic functions on I_n(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 I_n(r).

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

Petrov, P. (2015) Mean-Value Theorems for Harmonic Functions on the Cube in Rⁿ. Advances in Pure Mathematics, 5, 683-688. doi: 10.4236/apm.2015.511062.