The computation of orthogonal rational functions and their interpolating properties |
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Authors: | Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad |
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Institution: | (1) Department of Computer Science, K.U. Leuven, Belgium;(2) Department of Mathematical Analysis, University of La Laguna, Tenerife, Spain;(3) Department of Mathematics, University of Amsterdam, The Netherlands;(4) Department of Mathematics, University of Trondheim-NTH, Norway |
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Abstract: | We shall consider nested spacesl
n
,n = 0, 1, 21... of rational functions withn prescribed poles outside the unit disk of the complex plane. We study orthogonal basis functions of these spaces for a general positive measure on the unit circle. In the special case where all poles are placed at infinity,l
n
=
n
, the polynomials of degree at mostn. Thus the present paper is a study of orthogonal rational functions, which generalize the orthogonal Szegö polynomials. In this paper we shall concentrate on the functions of the second kind which are natural generalizations of the corresponding polynomials.The work of the first author is partially supported by a research grant from the Belgian National Fund for Scientific Research |
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Keywords: | Primary 42C05 Secondary 30D50 41A20 41A55 |
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