Convex Multivariate Approximation by Algebras of Continuous Functions

TL;DR

This paper extends a classical theorem to the multivariate convex approximation context, showing how algebras of continuous functions can be used for approximation in higher dimensions.

Contribution

It provides a multivariate convex approximation analog of Shvedov's theorem, advancing the theoretical understanding of function algebras.

Findings

Established an analog of Shvedov's theorem for multivariate convex approximation.

Demonstrated the applicability of algebras of continuous functions in higher-dimensional convex approximation.

Extended classical univariate approximation results to the multivariate setting.

Abstract

We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.