caa a22 4500 47583898X CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006409205633 doi (NATIONALLICENCE)springer-10.1023/A:1006409205633 Boundary Asymptotics for Orthogonal Rational Functions on the Unit Circle [Elektronische Daten] [Adhemar Bultheel, Patrick Van Gucht] Let w(θ) be a positive weight function on the unit circle of the complex plane. For a sequence of points { α k } k = 1 ∞ included in a compact subset of the unit disk, we consider the orthogonal rational functions φ n that are obtained by orthogonalization of the sequence { 1, z / π1, z 2 / π2, ... } where $$ {\pi }_k \left( {\rm Z} \right) = \prod\nolimits_{j^{ = 1} }^k {\left( {1 - \overline {\alpha } j{\rm Z}} \right)} $$ , with respect to the inner product $$\left\langle {f,g} \right\rangle = \frac{1}{{2{\pi }}}\int_{{ - \pi }}^{\pi } {f\left( {{e}^{i\theta } } \right)} \overline {g\left( {{e}^{i\theta } } \right)} w\left( {\theta } \right){d\theta }$$ In this paper we discuss the behaviour of φ n (t) for ∣ t ∣ = 1 and n → ∞ under certain conditions. The main condition on the weight is that it satisfies a Lipschitz-Dini condition and that it is bounded away from zero. This generalizes a theorem given by Szegő in the polynomial case, that is when all α k = 0. Kluwer Academic Publishers, 2000 orthogonal rational functions nationallicence asymptotics nationallicence Bultheel Adhemar Departement of Computer Science, K.U. Leuven, 3001, Heverlee, Belgium. e-mail aut Van Gucht Patrick Departement of Computer Science, K.U. Leuven, 3001, Heverlee, Belgium. e-mail aut Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 333-349 0167-8019 61:1-3<333 2000 61 10440 https://doi.org/10.1023/A:1006409205633 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006409205633 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bultheel Adhemar Departement of Computer Science, K.U. Leuven, 3001, Heverlee, Belgium. e-mail aut NATIONALLICENCE 700 1- Van Gucht Patrick Departement of Computer Science, K.U. Leuven, 3001, Heverlee, Belgium. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 333-349 0167-8019 61:1-3<333 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer