{"paper":{"title":"Multivariate Delta Goncarov and Abel 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":"2016-08-20T15:01:32Z","abstract_excerpt":"Classical Gon\\v{c}arov polynomials are polynomials which interpolate derivatives. Delta Gon\\v{c}arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gon\\v{c}arov polynomials and univariate delta Gon\\v{c}arov polynomials to the multivariate setting using umbral calculus. After introducing systems of delta operators, we define multivariate delta Gon\\v{c}arov polynomials, show that the associated interpolation problem is always solvable, and derive a generating functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05836","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"}