Umbral calculus in Ore extensions

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Benouaret, Chahrazed¹  Salinier, Alain² 

[1] USTHB, Fac Math, BP 32, El Alia 16111, Alger, Algeria

[2] Univ Limoges, Pole Math & Informat Limoges, Lab XLIM, UMR CNRS 7252, F-87060 Limoges, France

关键词: Coalgebra;    Difference algebra;    Ore extensions;    Pincherle calculus;    Translation operators;    Umbral calculus;   

DOI  :  10.1016/j.jpaa.2019.06.017

来源: Elsevier

【 摘 要 】

The aim of the paper is to show the existence of some ingredients for an umbral calculus on some Ore extensions, in a manner analogous to Rota's classical umbral calculus which deals with a univariate polynomial ring on a field of characteristic zero. For that, we introduce the notion of a quasi-derivation in order to specify Ore extensions on which building up this umbral calculus is possible. This allows in particular to define an action of the Ore extension on tensor products of modules. We develop also a Pincherle calculus for operators and we define a coalgebra structure on the Ore extension. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free