{"paper":{"title":"Generalized Goncarov polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Catherine H. Yan, Rudolph Lorentz, Salvatore Tringali","submitted_at":"2015-11-12T20:06:12Z","abstract_excerpt":"We introduce the sequence of generalized Gon\\v{c}arov polynomials, which is a basis for the solutions to the Gon\\v{c}arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon\\v{c}arov basis is a sequence $(t_n(x))_{n \\ge 0}$ of polynomials defined by the biorthogonality relation $\\varepsilon_{z_i}(\\mathfrak d^{i}(t_n(x))) = n! \\;\\! \\delta_{i,n}$ for all $i,n \\in \\mathbf N$, where $\\mathfrak d$ is a delta operator, $\\mathcal Z = (z_i)_{i \\ge 0}$ a sequence of scalars, and $\\varepsilon_{z_i}$ the evaluation at $z_i$. We present algebraic and analytic properties o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04039","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"}