Characterizations of woven frames

Bhandari, Animesh; Mukherjee, Saikat

doi:10.48550/arxiv.1809.09465

Cited by 3 publications

(4 citation statements)

References 20 publications

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“…Every frame sequence satisfies Bessel's inequlity, for detail discussion regarding the same we refer [4]. Analogous result is also satisfied for multiframelet.…”

Section: Resultsmentioning

confidence: 67%

Characterizations of Multiframelets on $\mathbb{Q}_{p}$

Haldar,

Bhandari

2019

Preprint

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This paper presents a discussion on p-adic multiframe by means of its wavelet structure, called as multiframelet, which is build upon p-adic wavelet construction. Multiframelets create much excitement in mathematicians as well as engineers on account of its tremendous potentiality to analyze rapidly changing transient signals. Moreover, multiframelets can produce more accurately localized temporal and frequency information, due to this fact it produce a methodology to reconstruct signals by means of decomposition technique. Various properties of multiframelet sequence in L 2 (Qp) have been analyzed. Furthermore, multiframelet set in Qp has been engendered and scrutinized.

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“…Every frame sequence satisfies Bessel's inequlity, for detail discussion regarding the same we refer [4]. Analogous result is also satisfied for multiframelet.…”

Section: Resultsmentioning

confidence: 67%

Characterizations of Multiframelets on $\mathbb{Q}_{p}$

Haldar,

Bhandari

2019

Preprint

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“…Definition 1.2. In H, two frames {f i } i∈I and {g i } i∈I are said to be woven if for every σ ⊂ I, {f i } i∈σ ∪ {g i } i∈σ c also forms a frame for H and the associated frame operator for every weaving is defined as [4],…”

Section: K-framementioning

confidence: 99%

Characterizations of Weaving K-frames

Bhandari¹,

Borah²,

Mukherjee³

2019

Preprint

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In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. This article focuses on study, characterization of weaving K-frames in different spaces. Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize woven-ness of Kframes.

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“…Weaving frames or woven frames were introduced by Bemrose et al in [1]. Later the concept of woven-ness has been characterized by Bhandari et al in [3] and characterization of weaving K-frames has been produced by Deepshikha et al in [7]. Definition 1.2.…”

Section: Introductionmentioning

confidence: 99%

“…Definition 1.2. [3] In H, two frames {f i } i∈I and {g i } i∈I are said to be woven if for every σ ⊂ I, {f i } i∈σ ∪ {g i } i∈σ c also forms a frame for H and the associated frame operator for every weaving is defined as,…”

Section: Introductionmentioning

confidence: 99%

On wovenness of K-fusion frames

Bhandari¹,

Mukherjee²

2019

Preprint

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In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-frame and fusion frame. Kfusion frames come naturally (having significant applications) when one needs to reconstruct functions (signals) from a large data in the range of a bounded linear operator. Getting inspiration from the concept of weaving frames in Hilbert space, we study the weaving form of Kfusion frames which have significant applications in wireless sensor networks. This article produces various characterizations of weaving Kfusion frames in different spaces. Furthermore, Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize woven-ness of the same.

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Characterizations of woven frames

Cited by 3 publications

References 20 publications

Characterizations of Multiframelets on $\mathbb{Q}_{p}$

Characterizations of Multiframelets on $\mathbb{Q}_{p}$

Characterizations of Weaving K-frames

On wovenness of K-fusion frames

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