Sobolev-orthogonal systems with tridiagonal skew-Hermitian differentiation matrices

A. Iserles, M. Webb

Research output: Contribution to journalArticlepeer-review


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 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 N coefficients can be computed in (Formula presented.) operations. © 2022 The Authors. Studies in Applied Mathematics published by Wiley Periodicals LLC.
Original languageEnglish
Pages (from-to)420-447
Number of pages28
JournalStudies in Applied Mathematics
Issue number2
Publication statusAccepted/In press - 2 Nov 2022


  • Malmquist–Takenaka functions
  • orthogonal systems
  • Sobolev orthogonality
  • spectral methods


Dive into the research topics of 'Sobolev-orthogonal systems with tridiagonal skew-Hermitian differentiation matrices'. Together they form a unique fingerprint.

Cite this