B-Gabor type frames in separable Hilbert spaces
It is guaranteed that Gabor like structured frames do exist in any finite dimensional Hilbert space via an invertible map from l2(ZN) J Thomas and Nambudiri [2022]. Hence the question: whether it is possible to obtain structured class of frames in separable Hilbert spaces? is relevant. In this artic...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2023-12-01
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| Series: | Ratio Mathematica |
| Subjects: | |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1236 |
| _version_ | 1827394863475195904 |
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| author | Thomas Jineesh N M Madhavan Namboothiri P N Jayaprasad |
| author_facet | Thomas Jineesh N M Madhavan Namboothiri P N Jayaprasad |
| author_sort | Thomas Jineesh |
| collection | DOAJ |
| description | It is guaranteed that Gabor like structured frames do exist in any finite dimensional Hilbert space via an invertible map from l2(ZN) J Thomas and Nambudiri [2022]. Hence the question: whether it is possible to obtain structured class of frames in separable Hilbert spaces? is relevant. In this article we obtain a structured class of frames for separable Hilbert spaces which are generalizations of Gabor frames for L2(R) in their construction aspects. We call them as B-Gabor type frames and present a characterization of the frame operators associated with these frames when B is a unitary map. Some significant properties of the associated frame operators are discussed. |
| first_indexed | 2024-03-08T18:21:24Z |
| format | Article |
| id | doaj.art-22e28d9d142c45fa89e7f7dd00e3a09e |
| institution | Directory Open Access Journal |
| issn | 1592-7415 2282-8214 |
| language | English |
| last_indexed | 2024-03-08T18:21:24Z |
| publishDate | 2023-12-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj.art-22e28d9d142c45fa89e7f7dd00e3a09e2023-12-30T21:04:20ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142023-12-0148010.23755/rm.v48i0.1236871B-Gabor type frames in separable Hilbert spacesThomas Jineesh0N M Madhavan Namboothiri1P N Jayaprasad2Mahatma Gandhi University Kerala IndiaMahatma Gandhi University Kerala IndiaMahatma Gandhi University Kerala IndiaIt is guaranteed that Gabor like structured frames do exist in any finite dimensional Hilbert space via an invertible map from l2(ZN) J Thomas and Nambudiri [2022]. Hence the question: whether it is possible to obtain structured class of frames in separable Hilbert spaces? is relevant. In this article we obtain a structured class of frames for separable Hilbert spaces which are generalizations of Gabor frames for L2(R) in their construction aspects. We call them as B-Gabor type frames and present a characterization of the frame operators associated with these frames when B is a unitary map. Some significant properties of the associated frame operators are discussed.http://eiris.it/ojs/index.php/ratiomathematica/article/view/1236gabor frameframe operatortranslationmodulation |
| spellingShingle | Thomas Jineesh N M Madhavan Namboothiri P N Jayaprasad B-Gabor type frames in separable Hilbert spaces Ratio Mathematica gabor frame frame operator translation modulation |
| title | B-Gabor type frames in separable Hilbert spaces |
| title_full | B-Gabor type frames in separable Hilbert spaces |
| title_fullStr | B-Gabor type frames in separable Hilbert spaces |
| title_full_unstemmed | B-Gabor type frames in separable Hilbert spaces |
| title_short | B-Gabor type frames in separable Hilbert spaces |
| title_sort | b gabor type frames in separable hilbert spaces |
| topic | gabor frame frame operator translation modulation |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1236 |
| work_keys_str_mv | AT thomasjineesh bgabortypeframesinseparablehilbertspaces AT nmmadhavannamboothiri bgabortypeframesinseparablehilbertspaces AT pnjayaprasad bgabortypeframesinseparablehilbertspaces |