Distributional equation for Laguerre-Hahn functionals on the unit circle
type: Item
instance of: scholarly article
title: Distributional equation for Laguerre-Hahn functionals on the unit circle
zbMATH Open document ID: 1180.33013
author: M. N. Rebocho
author: A. Branquinho
published in: Journal of Computational and Applied Mathematics
publication date: 2009-11-04T00:00:00Z
review text: The authors introduce the Laguerre-Hahn class of Hermitian functionals on the unit circle. The Laguerre-Hahn class on the real line has been studied by \textit{A. Magnus} [in: Padé approximation and its applications, Proc. Conf., Bad Honnef/Ger. 1983, Lect. Notes Math. 1071, 213--230 (1984; Zbl 0539.40003)] and \textit{P. Maroni} [in: Orthogonal polynomials and their applications, Proc. Int. Symp., Segovia/Spain 1986, Lect. Notes Math. 1329, 279--290 (1988; Zbl 0661.42015); C. R. Acad. Sci., Paris, Sér. I 313, No.~5, 209--212 (1991; Zbl 0736.33008)]. Analogously the authors establish the equivalence between a Riccati differential equation with polynomial coefficients for \(F\), \(zAF'=BF^2+CF+D\) and a distributional equation for a Hermitian linear functional \(u\), \({\mathcal D}(Au)=\widetilde{B} u^2+ \widetilde{C}u+ \widetilde{H}{\mathcal L}\), where \({\mathcal L}\) is the Lebesgue operator and \(\widetilde{B},\widetilde{C},\widetilde{H}\) are polynomials defined in terms of \(A,B,C,D\).
reviewed by: Chrysoula G. Kokologiannaki
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5624870
zbMATH Keywords: Hermitian functionals
zbMATH Keywords: Laguerre-Hahn functionals
zbMATH Keywords: measures on the unit circle
zbMATH Keywords: Carathéodory function
MaRDI profile type: Publication
full work available at URL: j.cam.2009.02.031
OpenAlex ID: W2073893581
cites work: Q3326167
cites work: Q3810313
cites work: Q4853625
cites work: Q5447424
cites work: Q3365598
cites work: \Delta -Coherent Pairs and Orthogonal Polynomials of a Discrete Variable
cites work: Second degree functionals on the unit circle
cites work: Q4061445
cites work: On the trigonometric moment problem
cites work: A special class of polynomials orthogonal on the unit circle including the associated polynomials
cites work: Q4306175
DOI: 10.1016/J.CAM.2009.02.031
description: scientific article; zbMATH DE number 5624870