{"paper":{"title":"Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yurii A. Neretin","submitted_at":"2005-05-10T15:54:15Z","abstract_excerpt":"We construct noncomplete orthogonal systems on the ray $[0,\\infty)$ that look like Jacobi polynomials $P_n(x)$ after a shift of degree $n\\mapsto n+a$, where $a$ is a real constant. These systems are solutions of some exotic Sturm-Liouville problem for hypergeometric differential operators.\n  We obtain the explicit spectral decomposition for these problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505188","kind":"arxiv","version":2},"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"}