Year: 2015
Type: preprint
Abstract: For functions defined on the $n$-dimensional hypercube $I_n (r) = \{\bm{x} \in \mathbb{R}^n ~\vert~ \vert x_i \vert \le r,~ i = 1, 2, \ldots , n\}$ and harmonic therein, we establish certain analogues of Gauss surface and volume mean-value formulas for harmonic functions on the ball in $\mathbb{R}^n$ and their extensions for polyharmonic functions. In particular, our results contribute to the best one-sided $L^1$-approximation by harmonic functions on $I_n (r)$.
Source: arXiv (Cornell University)
Author: Petrov, Petar
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1743225907