A Class of Orthogonal Refinable Functions and Wavelets

We give a construction, for any n 2, of a space S of spline functions of degree n – 1 with simple knots in (1/4)Z which is generated by a triple of refinable, orthogonal functions with compact support. Indeed, the result holds more generally by replacing the B-spline of degree n – 1 with simple knots at the integers by any continuous refinable function whose mask is a Hurwitz polynomial of degree n. A simple construction is also given for the corresponding wavelets.