{"paper":{"title":"$C_0$-semigroups of 2-isometries and Dirichlet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Eva A. Gallardo-Guti\\'errez, Jonathan R. Partington","submitted_at":"2018-06-18T16:45:47Z","abstract_excerpt":"In the context of a theorem of Richter, we establish a similarity between $C_0$-semigroups of analytic 2-isometries $\\{T(t)\\}_{t\\geq0}$ acting on a Hilbert space $\\mathcal H$ and the multiplication operator semigroup $\\{M_{\\phi_t}\\}_{t\\geq 0}$ induced by $\\phi_t(s)=\\exp (-st)$ for $s$ in the right-half plane $\\mathbb{C}_+$ acting boundedly on weighted Dirichlet spaces on $\\mathbb{C}_+$. As a consequence, we derive a connection with the right shift semigroup $\\{S_t\\}_{t\\geq 0}$ $$ S_tf(x)=\\left \\{ \\begin{array}{ll} 0 & \\mbox { if }0\\leq t\\leq x, \\\\ f(x-t)& \\mbox { if } x>t, \\end{array} \\right ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06816","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"}