{"paper":{"title":"Periodic distributions and periodic elements in modulation spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Elmira Nabizadeh, Joachim Toft","submitted_at":"2017-01-26T13:31:22Z","abstract_excerpt":"We characterize periodic elements in Gevrey classes, Gelfand-Shilov distribution spaces and modulation spaces, in terms of estimates of involved Fourier coefficients, and by estimates of their short-time Fourier transforms. If $q\\in [1,\\infty )$, $\\omega$ is a suitable weight and $(\\maclE _0^E)'$ is the set of all $E$-periodic elements, then we prove that the dual of $M^{\\infty ,q}_{(\\omega )}\\cap (\\maclE _0^E)'$ equals $M^{\\infty ,q'}_{(1/\\omega )}\\cap (\\maclE _0^E)'$ by suitable extensions of Bessel's identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07691","kind":"arxiv","version":4},"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"}