Stability of wavelet Frames and Riesz basis, with respect to translations in $L^p(R^n),1\le p <\infty$
Abstract
We consider the perturbation problem of wavelet frame (Riesz basis){'j,k,a0,b0} = {anj/20 '(aj0x − kb0)} about translation parameter b0 in Lp(Rn)−norm.If ' 2 S(Rn) ( Schwartz space ), we can estimate the frame bounds about theperturbation of translation parameter b0. Our results generalize the Balan’s [1] results.Our method and approach are different from Balan’s [1].
Copyright © 2012 Devendra Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. Kumar, Stability of wavelet Frames and Riesz basis, with respect to translations in $L^p(R^n),1\le p <\infty$, J. Math. Comput. Sci. 2 (2012), 593–603.
BibTeX
@article{Kumar2012,
author = {Kumar, Devendra},
title = {Stability of wavelet Frames and Riesz basis, with respect to translations in $L^p(R^n),1\le p <\infty$},
journal = {J. Math. Comput. Sci.},
volume = {2},
year = {2012},
pages = {593--603},
doi = {}
}