摘要
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).
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).
