{"paper":{"title":"Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Iker Gardeazabal-Guti\\'errez, Mateus Sousa","submitted_at":"2025-06-19T10:24:06Z","abstract_excerpt":"In this paper we present a criteria to obtain interpolations formulas in terms of the sequence $\\left(\\{T_n(f)(Nm)\\}\\}_{m\\in\\mathbb{Z}}\\right)_{n=1}^N$, where $f$ are functions whose Fourier transform is supported in $[-1/2,1/2]$, and $T_n$ are certain Fourier multiplier operators. We also discuss applications and also prove that our results recover several classical formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16195","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.16195/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}