Result: A criterion for uniqueness of a critical point inH 2 rational approximation: A criterion for uniqueness of a critical point in \(H_ 2\) rational approximation

Title:
A criterion for uniqueness of a critical point inH 2 rational approximation: A criterion for uniqueness of a critical point in \(H_ 2\) rational approximation
Authors:
Laurent Baratchart, Franck Wielonsky, Edward B. Saff
Source:
Journal d'Analyse Mathématique. 70:225-266
Publisher Information:
Springer Science and Business Media LLC, 1996.
Publication Year:
1996
Subject Terms:
Approximation by rational functions, uniqueness, critical point, 0101 mathematics, rational approximation, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1565-8538
0021-7670
DOI:
10.1007/bf02820445
Access URL:
https://hal.inria.fr/inria-00073822
https://hal.inria.fr/inria-00073822/document
https://link.springer.com/content/pdf/10.1007/BF02820445.pdf
https://link.springer.com/article/10.1007/BF02820445
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....f95f45e6a48f0863b0236ef9aef090d4
Database:
OpenAIRE

Further Information

This paper presents a criterion for uniqueness of a critical point in \(H_{2, R}\) rational approximation of type \((m,n)\), with \(m\geq n-1\). This criterion is differential-topological in nature, and turns out to be connected with corona equations and classical interpolation theory. This paper also gives its use with three examples, namely best approximation of fixed type on small circles, a de Montessus de Ballore type theorem, and diagonal approximation to the exponential function of large degree.