Weaving continuous generalized frames for operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909059605594112 |
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| author | Massit, Hafida Rossafi, Mohamed Park, Choonkil |
| author_facet | Massit, Hafida Rossafi, Mohamed Park, Choonkil |
| contents | Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the known results in continuous $L$-frames, weaving continuous and weaving continuous $ g$-frames, also we study weaving continuous $ L$-$g$-frames in Hilbert spaces.
Moreover, we study the behaviour continuous $ L$-$g$-frames under some perturbations, and we show that approximate $L$-duals are stable under small perturbation and that it is possible to remove some elements of a woven continuous $ L$-$g$-frame and still have a woven continuous $ L$-$g$-frame. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weaving continuous generalized frames for operators Massit, Hafida Rossafi, Mohamed Park, Choonkil Functional Analysis 41A58, 42C15, 46L05 Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the known results in continuous $L$-frames, weaving continuous and weaving continuous $ g$-frames, also we study weaving continuous $ L$-$g$-frames in Hilbert spaces. Moreover, we study the behaviour continuous $ L$-$g$-frames under some perturbations, and we show that approximate $L$-duals are stable under small perturbation and that it is possible to remove some elements of a woven continuous $ L$-$g$-frame and still have a woven continuous $ L$-$g$-frame. |
| title | Weaving continuous generalized frames for operators |
| topic | Functional Analysis 41A58, 42C15, 46L05 |
| url | https://arxiv.org/abs/2401.00969 |