Cyclic frames in finite-dimensional Hilbert spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916913890721792 |
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| author | Christensen, Ole Redhu, Navneet Shukla, Niraj K. |
| author_facet | Christensen, Ole Redhu, Navneet Shukla, Niraj K. |
| contents | Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic
frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi et al. in \cite{ACM} and subsequent papers; they are particularly interesting due to their
attractive properties in the context of erasure problems. By applying an alternative approach, we are able to shed new light on general dynamical frames as well as cyclic frames. In particular, we provide a characterization of dynamical frames, which in turn leads to
a characterization of cyclic frames. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclic frames in finite-dimensional Hilbert spaces Christensen, Ole Redhu, Navneet Shukla, Niraj K. Functional Analysis 42C15, 47B91 Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi et al. in \cite{ACM} and subsequent papers; they are particularly interesting due to their attractive properties in the context of erasure problems. By applying an alternative approach, we are able to shed new light on general dynamical frames as well as cyclic frames. In particular, we provide a characterization of dynamical frames, which in turn leads to a characterization of cyclic frames. |
| title | Cyclic frames in finite-dimensional Hilbert spaces |
| topic | Functional Analysis 42C15, 47B91 |
| url | https://arxiv.org/abs/2508.17088 |