{"paper":{"title":"On Gabor orthonormal bases over finite prime fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.CA","authors_text":"A. Iosevich, A. Mayeli, J. Pakianathan, M. Kolountzakis, Yu. Lyubarskii","submitted_at":"2017-12-25T19:40:56Z","abstract_excerpt":"We study Gabor orthonormal windows in $L^2({\\Bbb Z}_p^d)$ for translation and modulation sets $A$ and $B$, respectively, where $p$ is prime and $d\\geq 2$. We prove that for a set $E\\subset \\Bbb Z_p^d$, the indicator function $1_E$ is a Gabor window if and only if $E$ tiles and is spectral. Moreover, we prove that for any function $g:\\Bbb Z_p^d\\to \\Bbb C$ with support $E$, if the size of $E$ coincides with the size of the modulation set $B$ or if $g$ is positive, then $g$ is a unimodular function, i.e., $|g|=c1_E$, for some constant $c>0$, and $E$ tiles and is spectral. We also prove the existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09120","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"}