Sobolev-Orthogonal Systems with Tridiagonal Skew-Hermitian Differentiation Matrices
Classical Analysis and ODEs
2022-06-16 v1 Numerical Analysis
Numerical Analysis
Abstract
We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew-Hermitian differentiation matrix. While a theory of such L2-orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis. We characterise such systems completely as appropriately weighed Fourier transforms of orthogonal polynomials and present a number of illustrative examples, inclusive of a Sobolev-orthogonal system whose leading N coefficients can be computed in operations.
Cite
@article{arxiv.2206.07560,
title = {Sobolev-Orthogonal Systems with Tridiagonal Skew-Hermitian Differentiation Matrices},
author = {Arieh Iserles and Marcus Webb},
journal= {arXiv preprint arXiv:2206.07560},
year = {2022}
}