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https://hdl.handle.net/10316/11261
Title: | Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle | Authors: | Branquinho, A. Rebocho, M. N. |
Keywords: | Carathéodory function; Matrix Riccati differential equations; Matrix Sylvester differential equations; Semi-classical functionals; Measures on the unit circle | Issue Date: | 2008 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 08-16 (2008) | Abstract: | In this paper we characterize sequences of polynomials on the unit circle, orthogonal with respect to a Hermitian linear functional such that its corresponding Carath´eodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of matrix Sylvester differential equations. Furthermore, under certain conditions, we give a representation of such sequences in terms of semi-classical orthogonal polynomials on the unit circle. For the particular case of semi-classical orthogonal polynomials on the unit circle, a characterization in terms of first order differential systems is established. | URI: | https://hdl.handle.net/10316/11261 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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Matrix Sylvester equations in the theory of orthogonal polynomials.pdf | 192.22 kB | Adobe PDF | View/Open |
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