On Fourier Series in the Context of Jacobi Matrices
José M. A. Matos,
Paulo B. Vasconcelos,
José A. O. Matos
Affiliations
José M. A. Matos
Instituto Superior de Engenharia do Instituto Politécnico do Porto, Centro de Matemática da Universidade do Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Paulo B. Vasconcelos
Faculdade de Economia da Universidade do Porto, Centro de Matemática da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-464 Porto, Portugal
José A. O. Matos
Faculdade de Economia da Universidade do Porto, Centro de Matemática da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-464 Porto, Portugal
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.
