Potential Theory

doi:10.1007/978-1-84882-319-8

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Cited by 44 publications

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“…This note is devoted to formulas for calculation of integrals over the n-dimensional hypercube centered at 0 ( ) { } = ∂ , based on integration over hyperplanar subsets of n I and exact for harmonic or polyharmonic functions. They are presented in Section 2 and can be considered as natural analogues on n I of Gauss surface and volume mean-value formulas for harmonic functions ( [1]) and Pizzetti formula [2], ( [3], Part IV, Ch. 3, pp.…”

Section: Introductionmentioning

confidence: 99%

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

Petrov¹

2015

APM

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be a hypercube in n . We prove theorems concerning mean-values of harmonic and polyharmonic functions on () n I 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 n  and their extensions for polyharmonic functions. We also discuss an application of these formulas-the problem of best canonical one-sided L 1-approximation by harmonic functions on

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Section: Introductionmentioning

confidence: 99%