caa a22 4500 475838939 CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006433627981 doi (NATIONALLICENCE)springer-10.1023/A:1006433627981 Interpolation by Rational Functions with Nodes on the Unit Circle [Elektronische Daten] [Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad] From the Erdős-Turán theorem, it is known that if f is a continuous function on $$ {\Bbb T} = \left\{ {z:\left\lfloor z \right\rfloor = 1} \right\} $$ and L n (f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then $$ \mathop {\lim }\limits_{n \to \infty } \int_{\Bbb T} {\left| {f\left( z \right)} \right|^2 } \left| {{\text{d}}z} \right| = 0 $$ Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in $$ {\Bbb D} = \left\{ {z:\left| z \right| < 1} \right\} $$ and continuous on $$ {\Bbb D} \cup {\Bbb T} $$ and making use of algebraic interpolating polynomials in the roots of unity. In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent polynomials will be used as interpolants and, on the other hand, the interpolation points will be zeros of certain para-orthogonal functions with respect to a given measure on $$ {\Bbb T} $$ . Kluwer Academic Publishers, 2000 orthogonal rational functions nationallicence interpolation nationallicence R-Szegő quadrature nationallicence Bultheel Adhemar Department of Computer Science, KU Leuven, Belgium aut González-Vera Pablo Department of Mathematical Analysis, Universidad La Laguna, Tenerife, Spain aut Hendriksen Erik Department of Mathematics, University of Amsterdam, The Netherlands aut Njåstad Olav Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway aut Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 101-118 0167-8019 61:1-3<101 2000 61 10440 https://doi.org/10.1023/A:1006433627981 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006433627981 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bultheel Adhemar Department of Computer Science, KU Leuven, Belgium aut NATIONALLICENCE 700 1- González-Vera Pablo Department of Mathematical Analysis, Universidad La Laguna, Tenerife, Spain aut NATIONALLICENCE 700 1- Hendriksen Erik Department of Mathematics, University of Amsterdam, The Netherlands aut NATIONALLICENCE 700 1- Njåstad Olav Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 101-118 0167-8019 61:1-3<101 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer