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On wovenness of K-fusion frames

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Animesh Bhandari, Saikat Mukherjee

Functional Analysis · Submitted 13 Dec 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This article produces various characterizations of weaving K-fusion frames in different spaces.

how it is stated · asserted 1.00 read the record →

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arXiv ID1912.07530 (version 1)
Pith IDCE5D4Q5J, Pith's permanent record of this paper and its review
CitationAnimesh Bhandari, Saikat Mukherjee. "On wovenness of K-fusion frames." arXiv:1912.07530 (2019). https://pith.science/paper/CE5D4Q5J
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,292 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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. K-fusion 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 K-fusion frames which have significant applications in wireless sensor networks. This article produces various characterizations of weaving K-fusion frames in different spaces. Furthermore, Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize wovenness of the same.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.05 0.03 asserted 0.99
s1 K-fusion 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. background 1.00 0.08 0.03 asserted 0.97
s2 Getting inspiration from the concept of weaving frames in Hilbert space, we study the weaving form of K-fusion frames which have significant applications in wireless sensor networks. contribution 0.96 0.76 0.07 asserted 0.98
s3 This article produces various characterizations of weaving K-fusion frames in different spaces. contribution 0.98 0.93 0.32 asserted 1.00
s4 Furthermore, Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize wovenness of the same. contribution 0.83 0.90 0.13 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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. K-fusion 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 K-fusion frames which have significant applications in wireless sensor networks. This article produces various characterizations of weaving K-fusion frames in different spaces. Furthermore, Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize wovenness of the same.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 1 paper
  • Later the concept of woven-ness has been characterized by Bhandari et al. in [ref] and characterization of weaving $K$-frames has been produced by Deepshikha et al. in [ref] .

    Characterizations of woven frames · Woven and $K$-Woven Frame · 0.91

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