{"paper":{"title":"Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of Analytic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ugur Gul","submitted_at":"2010-02-24T21:27:43Z","abstract_excerpt":"In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as \"quasi-parabolic\". This is the class of composition operators on H^{2} with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form \\phi(z) = z+\\psi(z) where \\psi\\in H^{2}(\\mathbb{H}) and \\Im(\\psi(z)) >\\delta > 0. We especially examine the case where \\psi is discontinuous at infinity. A new method is devised to show that this type of composition operators fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4640","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"}