{"paper":{"title":"Explicit construction of non-stationary frames for $L^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michele Berra, Ubertino Battisti","submitted_at":"2015-09-04T13:13:29Z","abstract_excerpt":"We show the existence of a family of frames of $L^2(\\mathbb{R})$ which depend on a parameter $\\alpha\\in [0,1]$. If $\\alpha=0$, we recover the usual Gabor frame, if $\\alpha=1$ we obtain a frame system which is closely related to the so called DOST basis, first introduced by Stockwell and then analyzed by Battisti and Riba. If $\\alpha\\in (0,1)$, the frame system is associated to a so called $\\alpha$-partitioning of the frequency domain. Restricting to the case $\\alpha=1$, we provide a truly $n$-dimensional version of the DOST basis and an associated frame of $L^2(\\mathbb{R}^d)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01437","kind":"arxiv","version":2},"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"}