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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.03679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T21:07:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0acc3372b4608e06de31929b94d64192ceede1e394025cc474855277d15239ac","abstract_canon_sha256":"3dd96fd0ab7f57bbd5037105dc82e4cddc57605ab4fde78b158722b9ac0988d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:07.048728Z","signature_b64":"P4BZrefooenCDzzrQDSrQRf0nWkow2e49xgHBKf9sBAZJZK/qdnA8og7uMvTXEieufHfF6CK79dApfzXXzAwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b053fe289cfe07cf57a4e46bddbab702463a66fbe0e4a6bd114fd62ad56a77b8","last_reissued_at":"2026-05-18T01:27:07.048008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:07.048008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{Q}$. 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