{"paper":{"title":"Weak product spaces of Dirichlet series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Karl-Mikael Perfekt, Ole Fredrik Brevig","submitted_at":"2015-10-07T16:37:52Z","abstract_excerpt":"Let $\\mathscr{H}^2$ denote the space of ordinary Dirichlet series with square summable coefficients, and let $\\mathscr{H}^2_0$ denote its subspace consisting of series vanishing at $+\\infty$. We investigate the weak product spaces $\\mathscr{H}^2\\odot\\mathscr{H}^2$ and $\\mathscr{H}^2_0\\odot\\mathscr{H}^2_0$, finding that several pertinent problems are more tractable for the latter space. This surprising phenomenon is related to the fact that $\\mathscr{H}^2_0\\odot\\mathscr{H}^2_0$ does not contain the infinite-dimensional subspace of $\\mathscr{H}^2$ of series which lift to linear functions on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02019","kind":"arxiv","version":3},"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"}