On the extremal problem for entire functions

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• 作者：P. Yuditskii
• 关键词：Korkin&ndash ; Zolotarev theorem ; de Branges spaces ; Martin function ; Widom domains ; Approximation by entire functions ; Canonical systems ; Spectral theory
• 刊名：Journal of Approximation Theory
• 出版年：February, 2014
• 年：2014
• 卷：179
• 期：Complete
• 页码：63-93
• 全文大小：350 K

文摘

We generalize the Korkin-Zolotarev theorem to the case of entire functions having the smallest norm on a system of intervals . If 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.