On Fourier Series in the Context of Jacobi Matrices

Abstract

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.

Keywords

• orthogonal polynomials
• fourier series
• Jacobi matrix
• functions of matrices
• spectral methods