Repository logo
 

Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices

Published version
Peer-reviewed

Change log

Authors

Iserles, Arieh 
Webb, Marcus 

Abstract

jats:titleAbstract</jats:title>jats:pWe 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 Ljats:sub2</jats:sub> ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis. We characterize such systems completely as appropriately weighted Fourier transforms of orthogonal polynomials and present a number of illustrative examples, inclusive of a Sobolev‐orthogonal system whose leading jats:italicN</jats:italic> coefficients can be computed in  operations.</jats:p>

Description

Funder: Narodowe Centrum Nauki; Id: http://dx.doi.org/10.13039/501100004281


Funder: Simons Foundation; Id: http://dx.doi.org/10.13039/100000893

Keywords

4901 Applied Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Studies in Applied Mathematics

Conference Name

Journal ISSN

0022-2526
1467-9590

Volume Title

Publisher

Wiley