A linear algebra approach to monomiality and operational methods

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-18 DOI:10.1016/j.laa.2025.07.019

Luis Verde-Star

引用次数: 0

Abstract

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.

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一种线性代数方法的单一性和运算方法

本文利用线性代数方法得到了多项式空间上线性算子的一般结果，并利用多项式序列的单项式性质将这些结果应用于与多项式序列相关的算子。我们证明了所有这样的算子都是有限阶或无限阶的微分算子，具有多项式系数。我们考虑了与若干多项式序列相关的单态算子，如Appell和Sheffer，以及包括Meixner、Krawtchouk、Laguerre、Meixner- pollaczek和Hermite族的正交多项式序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.