Introduction

Pn(1) = 1, Pn(−1) = 0. (1.2) It is known that the refinement equation

φn(x) = n∑

2an,jφn(2x− j), x ∈ R, (1.3)

has a unique solution satisfying ∫∞ −∞ φn = 1. Moreover it is shown

in [5] that φn is continuous, non-negative and has support in [0, n]. In the special case Pn(z) = 2−n(z + 1)n, φn is the uniform B-spline of degree n − 1 with knots at 0, 1, . . . , n. We shall refer to φn as a refinable function with symbol Pn.