On the unicity of best \(L_ 1\)-approximation by polynomials of several variables (Q800585)

The problem of best \(L_ 1\)-approximation by polynomials of several variables for continuous rational functions on an open bounded connected subset K of \({\mathbb{R}}^ n\) is studied and the uniqueness of the approximation is proved. The author comments that the method of the paper is unlikely to give a solution to the corresponding problem for an element of the general subspace C(K). The main theorem of the paper is used to verify the uniqueness of the solutions on a rectangular region of a Korkin-Zolotarjov type extremal problem for polynomials of several variables and the explicit solution presented.