{"paper":{"title":"Uniformly convergent Fourier series and multiplication of functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"V. V. Lebedev","submitted_at":"2018-07-11T04:47:26Z","abstract_excerpt":"Let $U(\\mathbb T)$ be the space of all continuous functions on the circle $\\mathbb T$ whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in $U(\\mathbb T)$ does not always belongs to $U(\\mathbb T)$ even if one of the factors belongs to the Wiener algebra $A(\\mathbb T)$. In this paper we consider pointwise multipliers of the space $U(\\mathbb T)$, i.e., the functions $m$ such that $mf\\in U(\\mathbb T)$ whenever $f\\in U(\\mathbb T)$. We present certain sufficient conditions for a function to be a multiplier and also obtain some results of Salem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03949","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"}