Related papers: Weaving continuous generalized frames for operator…
Continuous generalized fusion frame theory was recently introduced by Rahimi and al. Several equalities and inequalities have been obtained for frame, fusion generalized fusion frame, among others. In the present paper, we continue and…
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the…
We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar to frames in a Hilbert space, we show that for any two approximate Schauder frames for a Banach space, every weaving is an approximate Schauder frame…
In this paper we introduce and investigate the concept of reproducing pairs which generalizes continuous frames. We will introduce a concept that represents a unifying way to look at certain continuous frames (resp. reproducing pairs) on…
After a short review of some basic facts on g-frames, we analyze in details the so-called (alternate) dual g-frames. We end the paper by introducing what we call {\em g-coherent states} and studying their properties.
We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…
The ability of Machine-Learning (ML) based model components to generalize to the previously unseen inputs, and the resulting stability of the models that use these components, has been receiving a lot of recent attention, especially when it…
We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…
Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. The Parseval frames are particularly useful and important, since they provide a simple reconstruction scheme and are…
In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian $g$, we will construct an uncountable family of…
Operator-valued frame ($G$-frame), as a generalization of frame is introduced by Kaftal, Larson, and Zhang in \textit{Trans. Amer. Math. Soc.}, 361(12):6349-6385, 2009 and by Sun in \textit{J. Math. Anal. Appl.}, 322(1):437-452, 2006. It…
Motivated by the dynamical sampling problem, we study frames in an infinite dimensional Hilbert space generated by the iterates of a bounded operator T, also known as dynamical frames. We first characterize the operators that generate…
In this paper, we introduce the concept of Continuous $\ast$-K-g-Frame in Hilbert $C^{\ast}$-Modules and we give some properties.
In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by…
We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…
This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a…
We address the conditions and design of controllers and observers for homogeneous networks of linear MIMO agents. We develop networked controllers and observers that ensure the stability of both the system state and the estimation error,…
We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…