{"paper":{"title":"Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA","math.RT","nlin.SI"],"primary_cat":"math.CA","authors_text":"Carlos \\'Alvarez-Fern\\'andez, Francisco Marcell\\'an, Gerardo Ariznabarreta, Juan Carlos Garc\\'ia-Ardila, Manuel Ma\\~nas","submitted_at":"2015-11-15T21:46:13Z","abstract_excerpt":"Given a matrix polynomial $W(x)$, matrix bi-orthogonal polynomials with respect to the sesquilinear form $\\langle P(x),Q(x)\\rangle_W=\\int P(x) W(x)\\operatorname{d}\\mu(x)(Q(x))^{\\top}$, $P(x),Q(x)\\in\\mathbb R^{p\\times p}[x]$, where $\\mu(x)$ is a matrix of Borel measures supported in some infinite subset of the real line, are considered. Connection formulas between the sequences of matrix bi-orthogonal polynomials with respect to $\\langle \\cdot,\\cdot\\rangle_W$ and matrix polynomials orthogonal with respect to $\\mu(x)$ are presented. In particular, for the case of nonsingular leading coefficients"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04771","kind":"arxiv","version":7},"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"}