On orthogonal systems of rational functions on the unit circle and polynomials orthogonal with respect to varying measures

• Autores: K. Pan
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Nº 3, 1993, pág. 313
• Idioma: inglés
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• Resumen

  • We study the recurrence relations of rational functions that are orthonormal on the unit circle and have all their poles in a given sequence of points outside the unit disk. These relations enable us to find the recurrence relations and the ratio asymptotic behaviors for the orthonormal polynomials with respect to varying weights dμn and dμn+1. At the end of this paper, we also consider the convergence theorem for multipoint Padé approximations of Markov type functions.