Wavelets on the integers.
In this paper the theory of wavelets on the integers is developed. For this, one needs to first find analogs of translations and dyadic dilations which appear in the classical theory. Translations in l2(Z) are defined in the obvious way, taking advantage of the additive group structure of the integers. Dyadic dilations, on the other hand, pose a greater problem. In the classical theory of wavelets on the real line, translation T and dyadic dilation T obey the commutativity relation DT^2 = TD. We...