Some theorems on best \(L_ 1\)-approximation of continuous functions (Q1059807)

This paper makes an attempt to unify the study of best \(L_ 1\)- approximation of vector-valued functions on convex bodies in \({\mathbb{R}}^ n\) by finite dimensional linear subspaces. Applying the results of the main theorem of the paper recaptures some known results as well as proving some new results. For example, one corollary is the uniqueness of best \(L_ 1\)-approximation of continuous complex-valued functions by different families of complex splines.