相关论文: Dual and multiplier of $K$-fusion frames

K-frames are strongly tools for the reconstruction elements from the range of a bounded linear operator K on a separable Hilbert space H. In this paper, we study some properties of K-frames and introduce the K-frame multipliers. We also…

K-frames, a new generalization of frames, were recently considered by L. Gavruta in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a…

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…

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…

Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…

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…

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…

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…

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…

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…

This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the notion of $K$-fusion frames. Characterizations of $K$-fusion…

We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…

The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in…

K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.

To achieve our main research goal, first we survey the approaches towards dual fusion frames existing in the literature and agree on the notion of duality for fusion frames in the sense of Kutyniok, Paternostro and Philipp ({\it Oper.…

In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral…

Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…

$K$-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled $K$-fusion frames, and we develop some results on the controlled $K$-fusion frames for…

In this article we introduce the notion of $J$-fusion frame for a Krein space $\mathbb{K}$. We relate this new concept with fusion frames for Hilbert spaces and also with $J$-frames for Krein spaces. We also approximate $J$-fusion frame…

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…