{"paper":{"title":"$2\\times 2$ Laguerre-type differential operator with triangular eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victoria Torres, Yanina Gonzalez","submitted_at":"2024-11-20T22:35:56Z","abstract_excerpt":"In this paper, we present a comprehensive account of all Laguerre-type differential operators $D$ that are symmetric with respect to a $2\\times 2$ irreducible weight $W$ on the interval $(0, \\infty)$. These operators are associated with monic orthogonal polynomials ${P_n}$, which satisfy the equation $DP_n = P_n\\Delta_n$ for a certain lower triangular eigenvalue $\\Delta_n$. We introduce three distinct families of operators and weights, each characterized by explicit expressions depending on two or three parameters, along with a new expression based on a single parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13736","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13736/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}