On the L1 extremal problem for entire functions

P. Yuditskii

doi:10.1016/j.jat.2013.11.011

On the ^L1 extremal problem for entire functions

P. Yuditskii

Johannes Kepler University Linz

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

4 Scopus citations

Abstract

We generalize the Korkin-Zolotarev theorem to the case of entire functions having the smallest ^L1 norm on a system of intervals E. If C{set minus}E is a domain of Widom type with the Direct Cauchy Theorem, we give an explicit formula for the minimal deviation. Important relations between the problem and the theory of canonical systems with reflectionless resolvent functions are shown.

Original language	English
Pages (from-to)	63-93
Number of pages	31
Journal	Journal of Approximation Theory
Volume	179
DOIs	https://doi.org/10.1016/j.jat.2013.11.011
State	Published - Feb 2014
Externally published	Yes

Bibliographical note

Funding Information:
The author was supported by the Austrian Science Fund FWF , project no: P22025-N18.

Funding

The author was supported by the Austrian Science Fund FWF , project no: P22025-N18.

Funders	Funder number
Austrian Science Fund FWF	P22025-N18

Keywords

Approximation by entire functions
Canonical systems
De Branges spaces
Korkin-Zolotarev theorem
Martin function
Spectral theory
Widom domains

Access to Document

10.1016/j.jat.2013.11.011

Cite this

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AB - We generalize the Korkin-Zolotarev theorem to the case of entire functions having the smallest L1 norm on a system of intervals E. If C{set minus}E is a domain of Widom type with the Direct Cauchy Theorem, we give an explicit formula for the minimal deviation. Important relations between the problem and the theory of canonical systems with reflectionless resolvent functions are shown.

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KW - De Branges spaces

KW - Korkin-Zolotarev theorem

KW - Martin function

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