{"paper":{"title":"Monomial expansions of $H_{p}$--functions in infinitely many variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Defant, Leonhard Frerick, Manuel Maestre, Pablo Sevilla-Peris","submitted_at":"2012-07-10T07:31:52Z","abstract_excerpt":"Each bounded holomorphic function on the infinite dimensional polydisk $\\mathbb{D}^\\infty$, $f \\in H_\\infty(\\mathbb{D}^\\infty)$, defines a formal monomial series expansion that in general does not converge to $f$. The set $\\mon H_\\infty(\\mathbb{D}^\\infty)$ contains all $ z $'s in which the monomial series expansion of each function $f \\in H_\\infty(\\mathbb{D}^\\infty)$ sums up to $f(z)$. Bohr, Bohnenblust and Hille, showed that it contains $\\ell_{2} \\cap \\mathbb{D}^\\infty$, but does not contain any of the slices $\\ell_{2+\\varepsilon} \\cap \\mathbb{D}^\\infty$. This was done in the context of Diric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2248","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"}