Approximation by Λ-Splines on the Circle

Abstract

Let Λ = {λ0,…, λn} denote a set of distinct integers and let Π(Λ) denote the set of all generalized polynomials of the formFor any given ζ on the unit circle U withwe consider the set Zk of points 1, ζ, ζ2, …, ζk−1 whereWe shall denote by or the class of Λ-splines S(z) which satisfy the following conditions:(i) S(z) ∊ Cn−1(U)(ii) S(z)|Av ∊ Π(Λ) where