Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

We generalize a major portion of the classical theory of Cand C embedded subspaces to pointfree topology, where the corresponding notions are frame Cand C -quotients. The central results characterize these quotients and generalize Urysohn’s Extension Theorem, among others. The proofs require calculations in CL, the archimedean f -ring of frame maps from the topology of the reals into the frame ...

We investigate frame theory over the binary field Z2, following work of Bodmann, Le, Reza, Tobi and Tomforde. We consider general finite dimensional vector spaces V over Z2 equipped with an (indefinite) inner product (·, ·)V which can be an arbitrary bilinear functional. We characterize precisely when two such spaces (V, (·, ·)V ) and (W, (·, ·)W ) are unitarily equivalent in the sense that the...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion fram...

Abstract. We discuss the structure of decoherence-free subsystems for a bosonic channel affected by collective depolarization. A single use of the channel is defined as a transmission of a pair of bosonic modes. Collective depolarization consists in a random linear U(2) transformation of the respective mode operators, which is assumed to be identical for N consecutive uses of the channel. We de...

In this paper we construct frames of Gabor type for the space Lrad(R ) of radial L-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a radial function. This construction is based on a generalization of the so called Feichtinger-Gröchenig theory – sometimes also called coorbit space theory – which was develo...

the objective of this review to be submitted in two independent parts, for steel frames and for rc frames, is to compare their structural performance with respect to the proposed n2-method, and so also of the consequent convenience of using pushover methodology for the seismic analysis of these structures. a preliminary investigation is presented on a pushover analysis used for the seismic perf...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.

The detection of a moving target using an IR-UWB Radar involves the core task of separating the waves reflected by the static background and by the moving target. This paper investigates the capacity of the low-rank and sparse matrix decomposition approach to separate the background and the foreground in the trend of UWB Radar-based moving target detection. Robust PCA models are criticized for ...