Umbral calculus in Ore extensions

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 quas...

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Veröffentlicht in:Journal of pure and applied algebra 2020-03, Vol.224 (3), p.958-986
Hauptverfasser: Benouaret, Chahrazed, Salinier, Alain
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2019.06.017