Examples of frames on the Cantor dyadic group

摘要

We present two ways to construct frames on the locally compact Cantor dyadic group. The first approach gives a Parseval frame related to the generalized Walsh-Dirichlet kernel, while the second approach includes the Daubechies-type "admissible condition" and leads to dyadic compactly supported wavelet frames. The corresponding wavelet constructions on the Cantor and Vilenkin groups (as well as on the half-line R_+) requires an additional constraint related to the requirement that the masks have no blocking sets.