Hermite—Birkhoff interpolation and approximation of a function and its derivatives

Abstract

In this paper we look at some fundamental results on Hermite and Hermite-Birkhoff interpolation by elements of Haar spaces and apply these to certain problems in the approximation of a function and its derivatives. Important interpolation results have been given by Ikebe [ 61 and Haussminn 14, 5 1. We shall use the main theorem of [ 5 ] to generalize the main theorem of (6 1. As an application we obtain information about the dimension of the set of best approximations of a function and its derivatives. An example is presented.