On a conjecture of Widom

Vilmos Totik; Peter Yuditskii

doi:10.1016/j.jat.2014.04.006

On a conjecture of Widom

Vilmos Totik
, Peter Yuditskii

University of Szeged
University of South Florida
Johannes Kepler University Linz

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In 1969 Harold Widom published his seminal paper (Widom, 1969) which gave a complete description of orthogonal and Chebyshev polynomials on a system of smooth Jordan curves. When there were Jordan arcs present the theory of orthogonal polynomials turned out to be just the same, but for Chebyshev polynomials Widom's approach proved only an upper estimate, which he conjectured to be the correct asymptotic behavior. In this note we make some clarifications which will show that the situation is more complicated.

Original language	English
Pages (from-to)	50-61
Number of pages	12
Journal	Journal of Approximation Theory
Volume	190
DOIs	https://doi.org/10.1016/j.jat.2014.04.006
State	Published - 1 Feb 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Funding

The authors thank S. Kalmykov and B. Nagy for bringing the paper [14] to their attention. The first author was supported by the European Research Council , Advanced Grant No. 267055 . The second author was supported by the Austrian Science Fund , project no: P22025-N18 .

Funders	Funder number
European Commission	267055
Austrian Science Fund	P22025-N18

Keywords

Chebyshev polynomials
Jordan arcs
Supremum norm
Widom's theory

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10.1016/j.jat.2014.04.006

Cite this

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On a conjecture of Widom

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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