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https://hdl.handle.net/10316/11261
Título: | Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle | Autor: | Branquinho, A. Rebocho, M. N. |
Palavras-chave: | Carathéodory function; Matrix Riccati differential equations; Matrix Sylvester differential equations; Semi-classical functionals; Measures on the unit circle | Data: | 2008 | Editora: | Centro de Matemática da Universidade de Coimbra | Citação: | Pré-Publicações DMUC. 08-16 (2008) | Resumo: | 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 | Direitos: | openAccess |
Aparece nas coleções: | FCTUC Matemática - Vários |
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Ficheiro | Descrição | Tamanho | Formato | |
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Matrix Sylvester equations in the theory of orthogonal polynomials.pdf | 192.22 kB | Adobe PDF | Ver/Abrir |
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