Affine and quasi-affine frames on positive half line

Abstract

Abstract. The notion of quasi-affine frame was recently introduced by Ron and Shen in order to achieve shift-invariance of the discrete wavelet transform. In this paper, we have extended the notion of affine and quasi-affine frame on Euclidean space $\mathbb R^n$ to positive half-line. Furthermore, we establish the relation between affine and quasi-affine frames on positive half line and the preservation of frame bounds when changing an affine frame to a quasi-affine frame is also shown.