Interpolation by rational functions with nodes on the unit circle

被引:6
作者
Bultheel, A [1 ]
González-Vera, P
Hendriksen, E
Njåstad, O
机构
[1] KU Leuven, Dept Comp Sci, Louvain, Belgium
[2] Univ La Laguna, Dept Math Anal, Tenerife, Spain
[3] Univ Amsterdam, Dept Math, NL-1012 WX Amsterdam, Netherlands
[4] Norwegian Univ Sci & Technol, Dept Math Sci, N-7034 Trondheim, Norway
关键词
orthogonal rational functions; interpolation; R-Szego quadrature;
D O I
10.1023/A:1006433627981
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
From the Erdos-Turan 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 (2 n + 1)th roots of unity, then [GRAPHICS] Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in D = {z : \z\ < 1} and continuous on bb D boolean OR 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.
引用
收藏
页码:101 / 118
页数:18
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