G-frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of timefrequency localization operators. Moreover, it was shown that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first pre...

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...

Abstract Few years ago Găvruţa gave the notions of K -frame and atomic system for a linear bounded operator in Hilbert space $$\mathcal {H}$$ H order to decompose {R}(K)$$ R ( K ) , range with frame-like expansion. Thes...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

Based on the shearlet transform we present a general construction of continuous tight frames for L(R) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From the results in [5] it follows that these systems enjoy the same desirable approximation properties for directional data as the bandl...

Abstract G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that...