On uniform approximation in \(\mathbb R^2\) of continuous Banach-valued functions
Given a Banach space \(X\), a family of linear operators \(V\) is constructed such that \(Vf\) is a uniform approximation to \(f\) for every continuous function \(f: {\mathbb R}^2 \to X\) having bounded variation in the sense of Hardy. Estimates of the error \(f-Vf\) in terms of the second order modulus of continuity \(\omega_2(f)\) are obtained. Some notations and the overall motivation of the article are unclear.
scientific article; zbMATH DE number 5122306