Orthonormal basis functions for continuous-time systems and \(L_p\) convergence
type: Item
instance of: scholarly article
title: Orthonormal basis functions for continuous-time systems and \(L_p\) convergence
zbMATH Open document ID: 0952.93020
DOI: 10.1007/PL00009854
author: Hüseyin Akçay
author: Brett Ninness
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2000-01-23T00:00:00Z
review text: The authors provide an analysis of the approximation properties of certain general classes of rational orthonormal basis functions. These bases generalize the Laguerre and Kautz cases. It is proved that the model sets are everywhere dense in the Hardy space \(H_1(\Pi)\) under the same conditions as those derived by the authors for denseness in \(H_p(\Pi)\), \(1< p< \infty\). As an extension, it is shown how to construct orthonormal model sets with prescribed asymptotic order that are everywhere dense in \(H_p(\Pi)\), \(1\leq p< \infty\). It is also shown that the Fourier series formed with the above basis converge in all spaces \(H_p(\Pi)\) and \(H_p(D)\), where \(D\) is the open unit disk and \(1< p< \infty\).
reviewed by: Liviu Goraş
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 93C30
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1348038
zbMATH Keywords: \(L_p\) convergence
zbMATH Keywords: rational orthonormal basis functions
zbMATH Keywords: Fourier series
MaRDI profile type: Publication
full work available at URL: pl00009854
OpenAlex ID: W2027070213
description: scientific article; zbMATH DE number 1348038