Interpolation by Rational Functions with Nodes on the Unit Circle |
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Authors: | Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad |
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Institution: | (1) Department of Computer Science, KU Leuven, Belgium;(2) Department of Mathematical Analysis, Universidad La Laguna, Tenerife, Spain;(3) Department of Mathematics, University of Amsterdam, The Netherlands;(4) Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway |
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Abstract: | From the Erds–Turán theorem, it is known that if f is a continuous function on
and L
n
(f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then
Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in
and continuous on
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
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Keywords: | orthogonal rational functions interpolation R-Szeg quadrature" target="_blank">gif" alt="odblac" align="BASELINE" BORDER="0"> quadrature |
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