On the Gauss transform of polynomial spline spaces (Q1263022)

``Two transformations of the space of polynomial splines of order m, belonging to a given set of knots, are investigated. In both cases the corresponding image spaces are Haar spaces. Using the B-spline basis one gets a transformed basis, consisting of restrictions of simple entire functions, satisfying a modified recursion formula. This transformation therefore can be used to construct best uniform approximations. Using the truncated power basis one gets a comparison theorem with an ordinary linear differential operator. This second transformation is suitable to gain a priori information concerning to minimal deviation in uniform approximation''