Weaving Hilbert space fusion frames

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g-frames. In this paper, we introduce fusion frames and g-frames in Hilbert C*-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g-frames in Hilbert spaces. We also show that tensor product of fusion frames (g-frames) is a fusion frame (g-frame) and tensor product of resolution of identity is a resolution of identity.

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Controlled g-fusion frame in Hilbert space

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691321500090 ◽

2021 ◽

pp. 2150009

Author(s):

Hanbing Liu ◽

Yongdong Huang ◽

Fengjuan Zhu

Keyword(s):

Hilbert Space ◽

Sufficient Conditions ◽

Iterative Algorithms ◽

Bessel Sequence ◽

Numerical Efficiency ◽

Fusion Frames ◽

Controlled Fusion ◽

Fusion Frame

Fusion frame is a generalization of frame, which can analyze signals by projecting them onto multidimensional subspaces. Controlled fusion frame as generalization of fusion frame, it can improve the numerical efficiency of iterative algorithms for inverting the fusion frame operators. In this paper, we first introduce the notion of controlled g-fusion frame, discuss several properties of controlled g-fusion Bessel sequence. Then, we present some sufficient conditions and some characterizations of controlled g-fusion frames. Finally, we study the sum of controlled g-fusion frames.

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Perturbations on K-fusion frames

Journal of Applied Analysis ◽

10.1515/jaa-2021-2044 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Animesh Bhandari ◽

Saikat Mukherjee

Keyword(s):

Hilbert Space ◽

Wireless Sensor Networks ◽

Sensor Networks ◽

Linear Operator ◽

Bounded Linear Operator ◽

Large Data ◽

Wireless Sensor ◽

Bounded Linear ◽

Fusion Frames

Abstract Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, for example, wireless sensor networks. In this paper, we discuss a generalization of fusion frames, K-fusion frames. K-fusion frames provide decompositions of a Hilbert space into atomic subspaces with respect to a bounded linear operator. This article studies various kinds of properties of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.

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G-frame representations with bounded operators

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691320500782 ◽

2020 ◽

pp. 2050078

Author(s):

Yavar Khedmati ◽

Fatemeh Ghobadzadeh

Keyword(s):

Hilbert Space ◽

Sufficient Conditions ◽

Bounded Operators ◽

Index Set ◽

Translation Invariant ◽

Fusion Frames ◽

Generalized Translation ◽

Special Cases ◽

Frame Representations

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form [Formula: see text], where [Formula: see text] belongs to Hilbert space [Formula: see text] and [Formula: see text] belongs to certain classes of bounded operators. Christensen et al. studied frames for [Formula: see text] with index set [Formula: see text] (or [Formula: see text]), that has representations in the form [Formula: see text] (or [Formula: see text]). As frames of subspaces, fusion frames and generalized translation invariant systems are the special cases of [Formula: see text]-frames, the purpose of this paper is to study and get sufficient conditions for [Formula: see text]-frames [Formula: see text] (or [Formula: see text] having the form [Formula: see text] [Formula: see text] (or [Formula: see text] [Formula: see text]). Also, we get the relation between representations of dual [Formula: see text]-frames with index set [Formula: see text]. Finally, we study stability of [Formula: see text]-frame representations under some perturbations.

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