{"paper":{"title":"Frame measures for infinitely many measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fariba Zeinal Zadeh Farhadi, Mohammad Reza Mardanbeigi, Mohammad Sadegh Asgari","submitted_at":"2019-05-18T05:44:02Z","abstract_excerpt":"For every frame spectral measure $ \\mu $, there exists a discrete measure $ \\nu $ as a frame measure. Since if $ \\mu $ is not a frame spectral measure, then there is not any general statement about the existence of frame measures $ \\nu $ for $ \\mu $, we were motivated to examine Bessel and frame measures. We construct infinitely many measures $ \\mu $ which admit frame measures $ \\nu $, and we show that there exist infinitely many frame spectral measures $ \\mu $ such that besides having a discrete frame measure, they admit continuous frame measures too."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07538","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"}