We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with effective support obeying the parabolic scaling principle length ≈ width. Our comparisons allow to extend Theorems known for one decomposition to others. We start from a Continuous Curvelet Transform f → Γf ...

We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a Hilbert space may be sampled to obtain a frame.

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

The present paper aims to study $c$-$g$-woven for Hilbert $C^ {*} $-module spaces, first, we give some definitions and fundamental properties which will be useful introduce the notion. And also of his are given. Finally, discuss perturbation $c$-$g$-woven.

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the...

Frame theory has a great revolution for recent years. This been extended from Hilbert spaces to C ∗ -modules. In this paper, we define and study the new concept of controlled continuous id="M6"> - id="M7"> K id="M8"> g -frames id="M9"> -modules establish some prope...