{"paper":{"title":"Linear spectral transformations for multivariate orthogonal polynomials and multispectral Toda hierarchies","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT","nlin.SI"],"primary_cat":"math.CA","authors_text":"Gerardo Ariznabarreta, Manuel Ma\\~nas","submitted_at":"2015-11-30T01:54:00Z","abstract_excerpt":"Linear spectral transformations of orthogonal polynomials in the real line, and in particular Geronimus transformations, are extended to orthogonal polynomials depending on several real variables. Multivariate Christoffel-Geronimus-Uvarov formulae for the perturbed orthogonal polynomials and their quasi-tau matrices are found for each perturbation of the original linear functional. These expressions are given in terms of quasi-determinants of bordered truncated block matrices and the 1D Christoffel-Geronimus-Uvarov formulae in terms of quotient of determinants of combinations of the original o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09129","kind":"arxiv","version":5},"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"}