Interpolation properties of rational functions of best mean square approximation on a circle and in a disk
type: Item
instance of: scholarly article
title: Interpolation properties of rational functions of best mean square approximation on a circle and in a disk
zbMATH Open document ID: 0857.30034
DOI: 10.1007/BF02309148
author: N. S. Vyacheslavov
author: A. K. Ramazanov
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: Consider the usual Hilbert space \(L_2(T)\) of square integrable functions with respect to the Lebesgue measure on the unit circle \(T\). The Cauchy transform of \(f\in L_2(T)\) defines an analytic function \(F\) in the unit disk and \(G\) in the complement of the unit disk. Mean square best rational approximation of \(f\) is considered of all possible degrees in the numerator and denominator. Such best approximants \(r\) are decomposed in simple fractions and separated the part with poles in the unit disk \(\tau\) from the part with poles on the exterior of the unit disk \(\lambda\) so that \(\tau + \lambda=r\). Exact results are provided on the extent to which \(\tau\) interpolates \(G\) and \(\lambda\) interpolates \(F\).
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 846478
zbMATH Keywords: mean square approximation
zbMATH Keywords: rational approximation
MaRDI profile type: Publication
cites work: Q3292706
cites work: Q5328270
cites work: Q5625542
cites work: Q3819295
cites work: Degree of rational functions of best approximation in \(L_ p(R^ m)\)
full work available at URL: https://doi.org/10.1007/bf02309148
OpenAlex ID: W2075074156
description: scientific article; zbMATH DE number 846478