Characterizations of weaving $K$-frames

Bhandari, Animesh; Borah, Debajit; Mukherjee, Saikat

doi:10.3792/pjaa.96.008

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…The concept of woven frames, which is motivated by some problems in signal processing [11], is used to write this linear combination by at least two frames. See [7,17,20,23,27,29] for more results on K-frames and weaving. Study and analysis of woven K-frames is the main purpose of this article.…”

Section: Introductionmentioning

confidence: 99%

New aspects of weaving K-frames: the excess and duality

Moghaddam

AREFİJAMAAL

2024

Hacettepe Journal of Mathematics and Statistics

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Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a $K^*$-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.

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Section: Introductionmentioning

confidence: 99%

New aspects of weaving K-frames: the excess and duality

Moghaddam

AREFİJAMAAL

2024

Hacettepe Journal of Mathematics and Statistics

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“…The present cosmological model contains this threeform field with (interacting, non-interacting) baryonic matter in the form of dust and radiation. Due to complicated form of the Einstein field Equations, the evolution equations are converted into an autonomous system by suitable choice of the dimensionless variables and non-hyperbolic equilibrium points are analyzed by Center manifold theory on the Hilbert space [18][19][20]. Bifurcation analysis [21] has been done to find the qualitative changes of global behavior due to different parameter values.…”

Section: Introductionmentioning

confidence: 99%

Dynamical system analysis of three-form field dark energy model with baryonic matter

2020

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A cosmological model having matter field as (non) interacting dark energy (DE) and baryonic matter and minimally coupled to gravity is considered in the present work with flat FLRW space time. The DE is chosen in the form of a three-form field while radiation and dust (i.e; cold dark matter) are the baryonic part. The cosmic evolution is studied through dynamical system analysis of the autonomous system so formed from the evolution equations by suitable choice of the dimensionless variables. The stability of the non-hyperbolic critical points are examined by Center manifold theory and possible bifurcation scenarios have been examined.

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On K-woven frames in Hilbert $$C^{*}$$-modules

Xiang

Chen

2022

J. Pseudo-Differ. Oper. Appl.

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Characterizations of weaving $K$-frames

Cited by 6 publications

References 13 publications

New aspects of weaving K-frames: the excess and duality

New aspects of weaving K-frames: the excess and duality

Dynamical system analysis of three-form field dark energy model with baryonic matter

On K-woven frames in Hilbert $$C^{*}$$-modules

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