Affine and Quasi-Affine Frames on Positive Half Line

The notion of quasi-affine frame was 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 Rn 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.