Title: Interpolation by rational functions with nodes on the unit circle
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: May-2000
Publisher: D. Reidel
Series Title: Acta applicandae mathematicae vol:61 issue:1-3 pages:101-118
Conference: International Conference of Rational Approximation and its Applications location:Antwep, Belgium date:6-11 June 1999
Abstract: From the Erdös-Turán theorem, it is known that if f is a continuous function on T={z:|z|=1} and L_n(f,z) denotes the unique Laurent polynomial interpolating f at the (2n+1)th roots of unity, then

lim_{n→∞} ∫_T |f(z)-L_n(f,z)|^2| |d z|=0.
Several years later, Walsh and Sharma gave a similar result but now considering a function analytic in D={z:|z|<1} and continuous on D U 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 T.
ISSN: 0167-8019
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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