{"paper":{"title":"Singular integrals, rank one perturbations and Clark model in general situation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Constanze Liaw, Sergei Treil","submitted_at":"2015-05-30T04:45:09Z","abstract_excerpt":"We start with considering rank one self-adjoint perturbations $A_\\alpha = A+\\alpha(\\,\\cdot\\,,\\varphi)\\varphi$ with cyclic vector $\\varphi\\in \\mathcal{H}$ on a separable Hilbert space $\\mathcal H$. The spectral representation of the perturbed operator $A_\\alpha$ is realized by a (unitary) operator of a special type: the Hilbert transform in the two-weight setting, the weights being spectral measures of the operators $A$ and $A_\\alpha$.\n  Similar results will be presented for unitary rank one perturbations of unitary operators, leading to singular integral operators on the circle.\n  This motivat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00072","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"}