We show that (bi-orthogonal) wavelet bases associated to a dilation matrix which is compatible with integer shifts are generally provided by a multi-resolution analysis. The proof is done by studying the projectors which commute with integer shifts.
Cite this article
Pierre Gilles Lemarié-Rieusset, Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions. Rev. Mat. Iberoam. 10 (1994), no. 2, pp. 283–347