以二元正交多项式为特征函数的高阶微分算子

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics Pub Date : 2025-04-14 DOI:10.1016/j.rinam.2025.100571

Misael E. Marriaga

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引用次数: 0

摘要

介绍了一种构造二元正交多项式为特征函数的高阶偏微分方程的系统方法。利用矩函数的框架，该方法不依赖于正交域的几何形状，使其广泛适用于不同的多项式族。给出了由低维流形上定义的测度修正的单位盘和三角形上的经典权函数的应用。

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Higher-order differential operators having bivariate orthogonal polynomials as eigenfunctions

We introduce a systematic method for constructing higher-order partial differential equations for which bivariate orthogonal polynomials are eigenfunctions. Using the framework of moment functionals, the approach is independent of the orthogonality domain’s geometry, enabling broad applicability across different polynomial families. Applications to classical weight functions on the unit disk and triangle modified by measures defined on lower-dimensional manifolds are presented.

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来源期刊

Results in Applied Mathematics Mathematics-Applied Mathematics

CiteScore

3.20

自引率

10.00%

发文量

审稿时长

23 days