{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-non-frame-property-of-gabor-systems","title":"On the non-frame property of Gabor systems with Hermite generators and the frame set conjecture","arxiv_id":"2311.01547","date":"2023-11-02","proceeding":null,"authors":["Andreas Horst","Jakob Lemvig","Allan Erlang Videbaek"],"abstract":"The frame set conjecture for Hermite functions formulated in [Gr\\\"ochenig, J. Fourier Anal. Appl., 20(4):865-895, 2014] states that the Gabor frame set for these generators is the largest possible, that is, the time-frequency shifts of the Hermite functions associated with sampling rates $\\alpha$ and modulation rates $\\beta$ that avoid all known obstructions lead to Gabor frames for $L^{2}(\\mathbb{R})$. By results in [Seip and Wallst\\'en, J. Reine Angew. Math., 429:107-113, 1992] and [Lemvig, Monatsh. Math., 182(4):899-912, 2017], it is known that the conjecture is true for the Gaussian, the $0$th order Hermite functions, and false for Hermite functions of order $2,3,6,7,10,11,\\dots$, respectively. In this paper we disprove the remaining cases except for the $1$st order Hermite function.","url_abs":"https://arxiv.org/abs/2311.01547v2","url_pdf":"https://arxiv.org/pdf/2311.01547v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-non-frame-property-of-gabor-systems","repo_url":"https://github.com/jakoblem/gfsp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}