ISSN:
1572-9265
Keywords:
Primary
;
42C05
;
Secondary
;
30D50
;
41A20
;
41A55
;
Rational interpolation
;
orthogonal functions
;
Szegö theory
;
Pick-Nevanlinna interpolation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02142207
