Distributional equation for Laguerre-Hahn functionals on the unit circle
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 \(A,B,C,D\).
scientific article; zbMATH DE number 5624870
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