{"paper":{"title":"Weighted composition operators on the Dirichlet space: boundedness and spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"E. A. Gallardo-Guti\\'errez, I. Chalendar, J.R. Partington","submitted_at":"2015-03-03T21:18:48Z","abstract_excerpt":"Boundedness of weighted composition operators $W_{u,\\varphi}$ acting on the classical Dirichlet space $\\mathcal{D}$ as $W_{u,\\varphi}f= u\\, (f\\circ \\varphi)$ is studied in terms of the multiplier space associated to the symbol $\\varphi$, i.e., ${\\mathcal{M}(\\phi)}=\\{ u \\in {\\mathcal D}: W_{u,\\phi} \\hbox{ is bounded on } {\\mathcal D} \\}$. A prominent role is played by the multipliers of the Dirichlet space. As a consequence, the spectrum of $W_{u,\\varphi}$ in $\\mathcal{D}$ whenever $\\varphi$ is an automorphism of the unit disc is studied, extending a recent work of Hyv\\\"arinen, Lindstr\\\"om, Nie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01130","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"}