A linear algebra approach to monomiality and operational methods

We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are differential operators, of finite or infinite order, with p...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 726; pp. 1 - 31
Main Author Verde-Star, Luis
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2025
Subjects
Generalized derivatives
Monomiality principle
Operational methods
Orthogonal polynomials
Sheffer polynomial sequences
15A30
33C45
Monomiality principle
44A45
Orthogonal polynomials
Generalized derivatives
Operational methods
Sheffer polynomial sequences
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Summary:We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are differential operators, of finite or infinite order, with polynomial coefficients. We consider the monomiality operators associated with several classes of polynomial sequences, such as Appell and Sheffer, and also orthogonal polynomial sequences that include the Meixner, Krawtchouk, Laguerre, Meixner-Pollaczek, and Hermite families.
ISSN:0024-3795
DOI:10.1016/j.laa.2025.07.019