{"paper":{"title":"Spectra of Some Weighted Composition Operators on $H^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carl Cowen, Derek Thompson, Eungil Ko, Feng Tian","submitted_at":"2014-05-20T17:56:00Z","abstract_excerpt":"We completely characterize the spectrum of a weighted composition operator $W_{\\psi, \\varphi}$ on $H^{2}(\\mathbb{D})$ when $\\varphi$ has Denjoy-Wolff point $a$ with $0<|\\varphi '(a)|< 1$, the iterates, $\\varphi_{n}$, converge uniformly to $a$, and $\\psi$ is in $H^{\\infty}(\\mathbb{D})$ and continuous at $a$. We also give bounds and some computations when $|a|=1$ and $\\varphi '(a)=1$ and, in addition, show that these symbols include all linear fractional $\\varphi$ that are hyperbolic and parabolic non-automorphisms. Finally, we use these results to eliminate possible weights $\\psi$ so that $W_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5173","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"}