H-sets in linear approximation

Abstract

This paper studies the role H-sets play in finding the best linear Tchebycheff approximation to a given continuous function. A simple definition is given for H-sets and the algebraic theory for linear approximation is developed. We find that many of the theorems where the Haar condition is supposed can be generalized in terms of H-sets; thus a general framework for Linear Tchebycheff Approximation is made.