Related papers: Weaving K-frames in Hilbert Spaces
A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas…
k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by…
In this paper, we focus on frames of operators or K-frames on Hilbert spaces in Parseval cases. Since equal-norm tight frames play important roles for robust data transmission, we aim to study this topics on Parseval K-frames. We will show…
K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…
We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…
Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special…
Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled $K$-frame in…
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a…
A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of…
In this paper, we will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames…
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…
Let $H_1$ and $H_2$ be two Hilbert spaces, $K$ and $L$ be bounded operatrors on $H_1$ and $H_2$ respectively. In this paper we study the relationship between $K$-frames for $H_1$ and $L$-frames for $H_2$ and $K\oplus L$-frames for…
Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
Weaving frames have potential applications in wireless sensor networks that require distributed processing of signal under different frames. In this paper, we study some new properties of weaving generalized frames (or $g$-frames) and…
Dual of K-frames in a right quaternionic Hilbert space has been recently introduced and studied by Ellouz[1]. In this paper, we study duals of K-frames and prove a characterization of a K-dual in terms of the canonical K-dual of a K-frame…
The concept of weaving of frames for Hilbert spaces was introduced by Bemrose et al. in 2016. Two frames $\{f_k\}_{k\in I}, \{g_k\}_{k\in I}$ are woven if the ``mixed system" $\{f_k\}_{k\in \sigma} \cup \{g_k\}_{k\in I\setminus \sigma}$ is…
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear…
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…
This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is…