{"paper":{"title":"Non-symmetric Jacobi and Wilson type polynomials","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Genkai Zhang, Lizhong Peng","submitted_at":"2005-11-29T15:47:08Z","abstract_excerpt":"Consider a root system of type $BC_1$ on the real line $\\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\\mathbb R$ to a $L^2$-space of $\\mathbb C^2$-valued functions on $\\mathbb R^+$ with the Harish-Chandra measure $|c(\\lam)|^{-2}d\\lam$.\n By introducing a weight function of the form $\\cosh^{-\\sig}(t)\\tanh^{2k} t$ on $\\mathbb R$ we find an orthogonal basis for the $L^2$-space on $\\mathbb R$ consisting of even and odd functions expressed in terms of the Jacobi polynomials (for each fixed $\\sig$ and $k$). We find a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511709","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"}