Stability of wavelet Frames and Riesz basis, with respect to translations in $L^p(R^n),1\le p

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].