Riesz MRA of dyadic dilations and the corresponding Riesz wavelet on LCA groups

Abstract

We have explored the concept of Riesz multiresolution analysis (Riesz MRA) on a locally compact Abelian group G, and have done a detailed study of the methods of construction of a Riesz wavelet from the given Riesz MRA. For simplicity, we have assumed the order of dilations to be two, i.e. we have worked with dyadic dilations. We have proved that precisely one function is required to construct a Riesz wavelet basis for the space L²(G).