Let Λ = {λ0,…, λ
n
} denote a set of distinct integers and let Π(Λ) denote the set of all generalized polynomials of the form
For any given ζ on the unit circle U with
we consider the set Zk
of points 1, ζ, ζ
2, …, ζ
k−1 where
We shall denote by or the class of Λsplines S(z) which satisfy the following conditions:

(i) S(z) ∊ C
n−1(U)

(ii) S(z)Av
∊ Π(Λ) where