arXiv subjects
Publications and source records attributed to Nikolay A. Shirokov.
We define H{ö}lder classes in the $L^p$ norm on a chord-arc curve in $\mathbb{R}^3$ and prove direct and inverse approximation theorems for functions from these classes by functions harmonic in a neighborhood of the curve. The approximation is estimated in the $L^p$ norm, and the smaller the neighborhood, the more accurate the approximation.
We give a constructive description of H{ö}lder-like classes of functions on chord-arc curves in $\mathbb{R}^3$ in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of those curve.
We give a constructive description of Hölder-like classes of functions on a chord-arc curve in $\mathbb{R}^3$ by means of a rate of approximation by function harmonic is shrinking neibourhoods of those curve