On umbral calculus. I
type: Item
instance of: scholarly article
title: On umbral calculus. I
zbMATH Open document ID: 0961.05004
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-12-14T00:00:00Z
review text: The author establishes some weaker characteristic conditions of the operator \(t_c\) and investigates invariant operators. It is shown that if an operator \(T\) can commute with one of the operators \(\sigma_p\) (\(p\neq 0\) and a root of unity), then \(T\) is an invariant operator. It is pointed out that the set of all invariant operators is a ring which is an algebra isomorphism with the ring of sequences of constants. A reverse result of the expansion theorem is also presented. The paper ends with presenting an open problem.
Mathematics Subject Classification ID: 05A40
zbMATH DE Number: 1449207
zbMATH Keywords: invariant operator
zbMATH Keywords: expansion theorem
zbMATH Keywords: open problem
author: Xiehua Sun
reviewed by: D. V. Chopra
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6686
OpenAlex ID: W2024934437
cites work: More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
cites work: Q3320678
cites work: Q4093447
cites work: On the foundations of combinatorial theory. VIII: Finite operator calculus
cites work: New characteristics of some polynomial sequences in combinatorial theory
DOI: 10.1006/JMAA.1999.6686
Recommended article: On umbral calculus
Recommended article: Q4209076
Recommended article: A selected survey of umbral calculus
Recommended article: Q3752388
Recommended article: An application of the umbral calculus
Recommended article: Umbral calculus and special functions
Recommended article: Q3320678
Recommended article: Q5231737
Recommended article: The umbral calculus
Recommended article: The Classical Umbral Calculus
description: scientific article; zbMATH DE number 1449207