{"paper":{"title":"Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E.V. Damaskinsky, V.V. Borzov","submitted_at":"2015-11-11T21:07:02Z","abstract_excerpt":"We consider two families of polynomials $\\mathbb{P}=\\polP$ and $\\mathbb{Q}=\\polQ$\\footnote{Here and below we consider only monic polynomials.} orthogonal on the real line with respect to probability measures $\\mu$ and $\\nu$ respectively. Let $\\polQ$ and $\\polP$ connected by the linear relations $$ Q_n(x)=P_n(x)+a_1P_{n-1}(x)+...+a_kP_{n-k}(x).$$ Let us denote $\\mathfrak{A}_P$ and $\\mathfrak{A}_Q$ generalized oscillator algebras associated with the sequences $\\mathbb{P}$ and $\\mathbb{Q}$. In the case $k=2$ we describe all pairs ($\\mathbb{P}$,$\\mathbb{Q}$), for which the algebras $\\mathfrak{A}_P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03679","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"}