Coherent Frames
Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally co...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2018-08-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdf |
| _version_ | 1819127886135689216 |
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| author | Ataollah Askari Hemmat Ahmad Safapour Zohreh Yazdani Fard |
| author_facet | Ataollah Askari Hemmat Ahmad Safapour Zohreh Yazdani Fard |
| author_sort | Ataollah Askari Hemmat |
| collection | DOAJ |
| description | Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of a single element of Hilbert space $mathcal{H}$ under some unitary representation $pi$ of $G$ on $mathcal{H}$. It is interesting that most of important frames are coherent. We investigate canonical dual and combinations of this frames |
| first_indexed | 2024-12-22T08:19:03Z |
| format | Article |
| id | doaj.art-c7fd5ea31fe04065b445cd569927bd1f |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-22T08:19:03Z |
| publishDate | 2018-08-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-c7fd5ea31fe04065b445cd569927bd1f2022-12-21T18:32:48ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002018-08-0111111110.22130/scma.2018.68276.26132195Coherent FramesAtaollah Askari Hemmat0Ahmad Safapour1Zohreh Yazdani Fard2Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, P.O.Box 76169-133, Kerman, Iran.Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran.Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of a single element of Hilbert space $mathcal{H}$ under some unitary representation $pi$ of $G$ on $mathcal{H}$. It is interesting that most of important frames are coherent. We investigate canonical dual and combinations of this frameshttp://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdfCoherent frameContinuous frameLocally compact groupUnitary representation |
| spellingShingle | Ataollah Askari Hemmat Ahmad Safapour Zohreh Yazdani Fard Coherent Frames Sahand Communications in Mathematical Analysis Coherent frame Continuous frame Locally compact group Unitary representation |
| title | Coherent Frames |
| title_full | Coherent Frames |
| title_fullStr | Coherent Frames |
| title_full_unstemmed | Coherent Frames |
| title_short | Coherent Frames |
| title_sort | coherent frames |
| topic | Coherent frame Continuous frame Locally compact group Unitary representation |
| url | http://scma.maragheh.ac.ir/article_32195_afa7e7e72abfe740af573ccc4c15cbac.pdf |
| work_keys_str_mv | AT ataollahaskarihemmat coherentframes AT ahmadsafapour coherentframes AT zohrehyazdanifard coherentframes |