Two Banach spaces of atoms for stable wavelet frame expansions

Two Banach spaces of atoms for stable wavelet frame expansions

In principle it is well known that for sufficiently nice wavelet functions the regularity of the wavelet transform allows to recover any L-function from its samples over any sufficiently dense, irregular sampling set. Equivalently, the (irregular) set of affine transforms of the given wavelet function forms a frame for L(R). In the present paper a systematic treatment of sufficient conditions f...

Frame Wavelet Sets and Wavelets in Banach Spaces

In this paper, we try to study a special class of frame wavelets in Banach spaces whose Fourier transforms are supported by frame wavelet sets. Our results generalize the various results of [2] to Banach spaces other than Hilbert spaces using the Feichtinger and Gröchenig theory. 2001 AMS Subject Classification : 42C99

Greedy expansions in Banach spaces

Types on stable Banach spaces

We prove a geometric characterization of Banach space stability. We show that a Banach space X is stable if and only if the following condition holds. Whenever X̂ is an ultrapower of X and B is a ball in X̂, the intersection B ∩X can be uniformly approximated by finite unions and intersections of balls in X; furthermore, the radius of these balls can be taken arbitrarily close to the radius of B,...

Stability of $g$-Frame Expansions

In this paper we investigate the stability of one-sided perturbation to g-frame expansions. We show that if $Lambda$ is a g-frame of a Hilbert space $mathcal{H}$, $Lambda_{i}^{a}=Lambda_{i}+Theta_{i}$ where $Theta_{i} in mathcal{L}(mathcal{H},mathcal{H}_{i})$, and $widetilde{f}=sum_{i in J}Lambda_{i}^{star}widetilde{Lambda}_{i}^{a}f$, $widehat{f}=sum_{i in J}(Lambda_{i}^{a})^{star}widetilde{Lam...