Strong and weak convergence of orthogonal systems of rational functions on the unit circle
نویسندگان
چکیده
منابع مشابه
Orthogonal rational functions and rational modifications of a measure on the unit circle
In this paper we present formulas expressing the orthogonal rational functions associated with a rational modification of a positive bounded Borel measure on the unit circle, in terms of the orthogonal rational functions associated with the initial measure. These orthogonal rational functions are assumed to be analytic inside the closed unit disc, but the extension to the case of orthogonal rat...
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The purpose of these lecture notes is to give a short introduction to the theory of orthogonal rational functions (ORF) on the unit circle. We start with the classical problem of linear prediction of a stochastic process to give a motivation for the study of Szegő’s problem and to show that in this context it will turn out that not as much the ORF but rather the reproducing kernels will play a ...
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We apply a theorem of Geronimus to derive some new formulas connecting Schur functions with orthogonal polynomials on the unit circle. The applications include the description of the associated measures and a short proof of Boyd’s result about Schur functions. We also give a simple proof for the above mentioned theorem of Geronimus. 1. Schur functions In what follows we adopt the following nota...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1993
ISSN: 0377-0427
DOI: 10.1016/0377-0427(93)90038-d