Gramian Analysis of Affine Bases and Affine Frames

摘要

Shift invariance fiberization techniques are applied for the study of thesynthesis and analysis operators of affine (wavelet) systems. In this approach, one has first to circumvent the fact that affine systems are not shift invariant. The results obtained include characterizations of the Bessel property, the Riesz basis property and the frame property of such sets in terms of the behaviour of simpler operators. Various estimates of the lower and upper frame (Riesz) bounds are included, too.