@article{2a4c3159cd7b4097a18b5eca2fc74c27,

title = "Sobolev-orthogonal systems with tridiagonal skew-Hermitian differentiation matrices",

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 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. {\textcopyright} 2022 The Authors. Studies in Applied Mathematics published by Wiley Periodicals LLC.",

keywords = "Malmquist–Takenaka functions, orthogonal systems, Sobolev orthogonality, spectral methods",

author = "A. Iserles and M. Webb",

note = "Export Date: 13 March 2023 Correspondence Address: Webb, M.; Department of Mathematics, Alan Turing Building, United Kingdom; email: marcus.webb@manchester.ac.uk Funding details: Simons Foundation, SF, 663281 Funding details: Polska Akademia Nauk, PAN Funding text 1: The authors are grateful for very useful and enlightening correspondence with Enno Diekma, Erik Koelink, and Tom Koornwinder. We gratefully acknowledge the partial support by the Simons Foundation Award No 663281 granted to the Institute of Mathematics of the Polish Academy of Sciences for the years 2021–2023. MW acknowledges support by Computational Mathematics in Quantum Mechanics, Grant of the National Science Centre (SONATA‐BIS), project no. 2019/34/E/ST1/00390.",

year = "2022",

month = nov,

day = "2",

doi = "10.1111/sapm.12544",

language = "English",

volume = "150",

pages = "420--447",

journal = "Studies in Applied Mathematics",

issn = "1467-9590",

publisher = "John Wiley & Sons Ltd",

number = "2",

}