Frames, biorthogonal dual and other properties associated with wavelet system on ℝ

Abstract

It is well known that the system of translates in [Formula: see text] has been characterized as Bessel sequences, frames and Riesz bases in terms of the Fourier transform. The aim of this paper is to obtain similar types of characterization for the wavelet system emerging out of integer translations and dyadic dilations. The existence of the biorthogonal dual system and nonredundancy properties of the wavelet system are also investigated here.