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.
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页数：16
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