{"paper":{"title":"Composition Operators on Bohr-Bergman Spaces of Dirichlet Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Maxime Bailleul, Ole Fredrik Brevig","submitted_at":"2014-09-10T10:49:42Z","abstract_excerpt":"For $\\alpha \\in \\mathbb{R}$, let $\\mathscr{D}_\\alpha$ denote the scale of Hilbert spaces consisting of Dirichlet series $f(s) = \\sum_{n=1}^\\infty a_n n^{-s}$ that satisfy $\\sum_{n=1}^\\infty |a_n|^2/[d(n)]^\\alpha < \\infty$. The Gordon--Hedenmalm Theorem on composition operators for $\\mathscr{H}^2=\\mathscr{D}_0$ is extended to the Bergman case $\\alpha>0$. These composition operators are generated by functions of the form $\\Phi(s) = c_0 s + \\varphi(s)$, where $c_0$ is a nonnegative integer and $\\varphi(s)$ is a Dirichlet series with certain convergence and mapping properties. For the operators wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3017","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":""},"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"}