{"paper":{"title":"Unitary discrete Hilbert transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Kristian Seip, Tesfa Y. Mengestie, Yurii Belov","submitted_at":"2009-11-02T14:08:20Z","abstract_excerpt":"Weighted discrete Hilbert transforms $(a_n)_n \\mapsto \\big(\\sum_n a_n v_n/(\\lambda_j-\\gamma_n)\\big)_j$ from $\\ell^2_v$ to $\\ell^2_w$ are considered, where $\\Gamma=(\\gamma_n)$ and $\\Lambda=(\\lambda_j)$ are disjoint sequences of points in the complex plane and $v=(v_n)$ and $w=(w_j)$ are positive weight sequences. It is shown that if such a Hilbert transform is unitary, then $\\Gamma\\cup\\Lambda$ is a subset of a circle or a straight line, and a description of all unitary discrete Hilbert transforms is then given. A characterization of the orthogonal bases of reproducing kernels introduced by L. d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0318","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"}