{"paper":{"title":"Uniqueness sets for functions of Dirichlet-type with restricted Taylor coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Daniel Seco, Nazar Miheisi","submitted_at":"2026-06-16T10:02:05Z","abstract_excerpt":"Let $H$ be a reproducing kernel Hilbert space over the unit disk $\\mathbb{D}$, where analytic monomials span a dense subset. Given $\\mathcal{N} \\subseteq\\mathbb{Z}_+$ and $\\Lambda \\subseteq \\mathbb{D}$ we say that $(\\Lambda,\\mathcal{N})$ is a uniqueness pair for $H$ if $\\Lambda$ is a uniqueness set for the subspace of $H$ spanned by $\\{z^n:\\;n\\in\\mathcal{N}\\}$. We examine uniqueness pairs in the Dirichlet-type spaces $\\mathbb{D}_\\alpha$, $0\\leq\\alpha\\leq1$. We prove two complementary results. First, if $\\mathcal{N}$ contains sufficiently long finite arithmetic progressions with fixed gap size,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17740","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17740/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"}