Construction of a Riesz Wavelet Basis on Locally Compact Abelian Groups

Abstract

We have explored the concept of Riesz multiresolution analysis on a locally compact Abelian group G, and have extensively studied the methods of construction of a Riesz wavelet from the given Riesz MRA. We have proved that, if δα is the order of dilation, then precisely δα−1 functions are required to construct a Riesz wavelet basis for L²(G). An example, supporting our theory and illustrating the methods developed, has also been discussed in detail.

Key words and phrases. LCA Groups, Riesz Basis, Multiresolution Analysis, order of dilation, refinement equation.

2000 Mathematics Subject Classification. 42C40, 22B05