A new family of hyperbolic slits in the Gabor frame set of B-spline generators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915723577655296 |
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| author | Lemvig, Jakob |
| author_facet | Lemvig, Jakob |
| contents | We exhibit a new infinite family of hyperbolic curves in the complement of the frame set of Gabor systems with B-spline generators. The proof technique is a combination of an approach by Gröchenig [Partitions of unity and new obstructions for Gabor frames, arXiv:1507.08432, 2015] and a partly partition of unity argument by Nielsen and the author [Counterexamples to the B-spline conjecture for Gabor frames, J. Fourier Anal. Appl., 22(6):1440-1451, 2016]. We relate the new hyperbolic obstructions to the "right bow tie" of the so-called Janssen tie [Zak transforms with few zeros and the tie, In Advances in Gabor analysis, Birkhäuser, 2003]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new family of hyperbolic slits in the Gabor frame set of B-spline generators Lemvig, Jakob Functional Analysis 42C15 We exhibit a new infinite family of hyperbolic curves in the complement of the frame set of Gabor systems with B-spline generators. The proof technique is a combination of an approach by Gröchenig [Partitions of unity and new obstructions for Gabor frames, arXiv:1507.08432, 2015] and a partly partition of unity argument by Nielsen and the author [Counterexamples to the B-spline conjecture for Gabor frames, J. Fourier Anal. Appl., 22(6):1440-1451, 2016]. We relate the new hyperbolic obstructions to the "right bow tie" of the so-called Janssen tie [Zak transforms with few zeros and the tie, In Advances in Gabor analysis, Birkhäuser, 2003]. |
| title | A new family of hyperbolic slits in the Gabor frame set of B-spline generators |
| topic | Functional Analysis 42C15 |
| url | https://arxiv.org/abs/2601.07642 |