{"paper":{"title":"Asymptotic boundary forms for tight Gabor frames and lattice localization domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H.G. Feichtinger, K. Nowak, M. Pap","submitted_at":"2015-01-22T13:47:53Z","abstract_excerpt":"We consider Gabor localization operators $G_{\\phi,\\Omega}$ defined by two parameters, the generating function $\\phi$ of a tight Gabor frame $\\{\\phi_\\lambda\\}_{\\lambda \\in \\Lambda}$, parametrized by the elements of a given lattice $\\Lambda \\subset \\Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\\Bbb{R}^2$, and a lattice localization domain $\\Omega \\subset \\Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\\Lambda$. We find an explicit formula for the boundary form $BF(\\phi,\\Omega)=\\text{A}_\\Lambda \\lim_{R\\rightarrow \\infty}\\frac{PF(G_{\\phi,R\\Omega})}{R}$, the norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05496","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}