Orthogonal wavelets on direct products of cyclic groups

We describe a method for constructing Compactly Supported orthogonal wavelets on a locally compact Abelian group G which is the weak direct product of a countable set of cyclic groups of pth order. For all integers p,n >= 2, we establish necessary and sufficient conditions under which the Solutions of the corresponding scaling equations with p(n) numerical coefficients generate multiresolution analyses in L-2 (G). It is noted that the coefficients of these scaling equations can be calculated from the given values of p(n) parameters using the discrete Vilenkin-Chrestenson transform. Besides, we obtain conditions under which a compactly Supported solution of the scaling equation in L-2(G) is stable and has a linearly independent system of "integer" shifts. We present several examples illustrating these results.