Structural formulas for a family of matrix valued Laguerre polynomials and applications

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-01-16 DOI:10.1016/j.aam.2025.102851

Andrea L. Gallo

引用次数: 0

Abstract

In this work, we study matrix valued orthogonal polynomials (MVOPs) with respect to a Laguerre-type matrix weight. We derive difference-differential relations for these MVOPs and provide explicit expressions for their entries using classical Laguerre polynomials. Under some shifting hypothesis, we demonstrate that the entries of the associated MVOPs can be expressed in terms of dual-Hahn polynomials. Additionally, we give an LDU decomposition for the squared norms of the MVOPs. As an application we study deformed weights and Toda-type equations.

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一类矩阵值拉盖尔多项式的结构公式及其应用

在这项工作中，我们研究了关于拉盖尔型矩阵权值的矩阵值正交多项式（MVOPs）。我们推导了这些MVOPs的微分-微分关系，并使用经典的拉盖尔多项式给出了它们的显式表达式。在一些移位假设下，我们证明了相关MVOPs的条目可以用双hahn多项式表示。此外，我们给出了MVOPs的平方范数的LDU分解。作为应用，我们研究了变形权和toda型方程。

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

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.