{"paper":{"title":"Christoffel formula for kernel polynomials on the unit circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei Mart\\'inez-Finkelshtein, A. Sri Ranga, Cleonice F. Bracciali, Daniel O. Veronese","submitted_at":"2017-01-18T10:07:10Z","abstract_excerpt":"Given a nontrivial positive measure $\\mu$ on the unit circle, the associated Christoffel-Darboux kernels are $K_n(z, w;\\mu) = \\sum_{k=0}^{n}\\overline{\\varphi_{k}(w;\\mu)}\\,\\varphi_{k}(z;\\mu)$, $n \\geq 0$, where $\\varphi_{k}(\\cdot; \\mu)$ are the orthonormal polynomials with respect to the measure $\\mu$. Let the positive measure $\\nu$ on the unit circle be given by $d \\nu(z) = |G_{2m}(z)|\\, d \\mu(z)$, where $G_{2m}$ is a conjugate reciprocal polynomial of exact degree $2m$. We establish a determinantal formula expressing $\\{K_n(z,w;\\nu)\\}_{n \\geq 0}$ directly in terms of $\\{K_n(z,w;\\mu)\\}_{n \\geq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04995","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"}