 Orthonormal rational functions on a semi-infinite intervalJianqiang Liu Applied Mathematics and Computation, 2024, vol. 479, issue C Abstract: In this paper we propose a novel family of weighted orthonormal rational functions on a semi-infinite interval. We write a sequence of integer-coefficient polynomials in several forms and derive their corresponding differential equations. These equations do not form Sturm-Liouville problems. We overcome this disadvantage by multiplying some factors, resulting in a sequence of irrational functions. We deduce various generating functions of this sequence and find the associated Sturm-Liouville problems, which bring orthogonality. Then we establish a Hilbert space of functions defined on a semi-infinite interval with an inner product induced by a weight function determined by the Sturm-Liouville problems mentioned above. The even subsequence of the irrational function sequence above forms an orthonormal basis for this space. The Fourier expansions of some power functions are deduced. The sequence of non-positive integer power functions forms a non-orthogonal basis for this Hilbert space. We give two examples, one example of Fourier expansion and one example of interpolation as applications. Keywords: Orthonormal basis; Rational function; Semi-infinite interval; Chebyshev polynomial; Riemann-Lebesgue lemma (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003485 DOI: 10.1016/j.amc.2024.128887 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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