On the Stability of Frames and Riesz Bases

AbstractThe first part of this paper supplements the recent work of Heil and Christensen on the stability of frames in Banach and Hilbert spaces. After obtaining a multivariate version of Kadec′s 1/4-theorem (which is used in the sequel), two of Christensen′s results, Chui and Shi′s Second Oversampling Theorem, and a variety of other results and techniques are applied to study the stability of multivariate exponential, wavelet, and Gabor frame and Riesz bases. Specific frame bounds and quantitative conditions of validity for mother wavelet and sampling perturbations are given