{"paper":{"title":"An infinite dimensional umbral calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dmitri Finkelshtein, Eugene Lytvynov, Maria Joao Oliveira, Yuri Kondratiev","submitted_at":"2017-01-16T15:25:28Z","abstract_excerpt":"The aim of this paper is to develop foundations of umbral calculus on the space $\\mathcal D'$ of distributions on $\\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\\mathcal D'$. We define a sequence of monic polynomials on $\\mathcal D'$, a polynomial sequence of binomial type, and a Sheffer sequence. We present equivalent conditions for a sequence of monic polynomials on $\\mathcal D'$ to be of binomial type or a Sheffer sequence, respectively. We also construct a lifting of a sequence of monic polynomials on $\\mathbb R$ of binomial type to a polynomial sequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04326","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"}