Block-equivalent finite Gabor frames
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913132859883520 |
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| author | Asipchuk, Oleg De Carli, Laura Rodriguez, Luis |
| author_facet | Asipchuk, Oleg De Carli, Laura Rodriguez, Luis |
| contents | We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent.
We show that a Gabor system $\mathcal{G}=\mathcal{G}(g,L\times K)\subset \mathbb C^N$ is block-equivalent when either the modulation set $L$ or the translation set $K$ is a subgroup of $\mathbb Z_N$. We also characterize situations in which the frame operator matrix becomes diagonal.
Finally, we show that geometric conditions on subsets of $\mathbb Z_N$ force certain diagonals of the frame operator matrix of $\mathcal{G}$ to vanish, yielding additional sparsity and block structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16139 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Block-equivalent finite Gabor frames Asipchuk, Oleg De Carli, Laura Rodriguez, Luis Functional Analysis 42C15, 15B05 (Primary) 11B75 (Secondary) We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a Gabor system $\mathcal{G}=\mathcal{G}(g,L\times K)\subset \mathbb C^N$ is block-equivalent when either the modulation set $L$ or the translation set $K$ is a subgroup of $\mathbb Z_N$. We also characterize situations in which the frame operator matrix becomes diagonal. Finally, we show that geometric conditions on subsets of $\mathbb Z_N$ force certain diagonals of the frame operator matrix of $\mathcal{G}$ to vanish, yielding additional sparsity and block structures. |
| title | Block-equivalent finite Gabor frames |
| topic | Functional Analysis 42C15, 15B05 (Primary) 11B75 (Secondary) |
| url | https://arxiv.org/abs/2605.16139 |