Gibbs' phenomenon for nonnegative compactly supported scaling vectors

This paper considers Gibbs' phenomenon for scaling vectors in L2(R). We first show that a wide class of multiresolution analyses suffer from Gibbs' phenomenon. To deal with this problem, in [Contemp. Math. 216 (1998) 63-79], Walter and Shen use an Abel summation technique to construct a positive scaling function Pr, 0