On Fourier Series in the Context of Jacobi Matrices

被引：0

作者：

Matos, Jose M. A. ^{[1
]}

Vasconcelos, Paulo B. ^{[2
]}

Matos, Jose A. O. ^{[2
]}

机构：

[1] Univ Porto, Inst Super Engn, Inst Politecn Porto, Ctr Matemat, Rua Dr Antonio Bernardino de Almeida 431, P-4249015 Porto, Portugal

[2] Univ Porto, Fac Econ, Ctr Matemat, Rua Dr Roberto Frias S-N, P-4200464 Porto, Portugal

来源：

AXIOMS | 2024年 / 13卷 / 09期

关键词：

orthogonal polynomials; fourier series; Jacobi matrix; functions of matrices; spectral methods; CONNECTION COEFFICIENTS; LINEARIZATION FORMULAS; POLYNOMIALS;

D O I：

10.3390/axioms13090581

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the properties of matrices that emerge from the application of Fourier series to Jacobi matrices. Specifically, we focus on functions defined by the coefficients of a Fourier series expressed in orthogonal polynomials. In the operational formulation of integro-differential problems, these infinite matrices play a fundamental role. We have derived precise calculation formulas for their elements, enabling exact computation of these operational matrices. Numerical results illustrate the effectiveness of our approach.

引用

页数：16

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