On the L1 extremal problem for entire functions

被引：4
|
作者：
Yuditskii, P. [1 ]
机构：
[1] Johannes Kepler Univ Linz, Abt Dynam Syst & Approximationstheorie, A-4040 Linz, Austria
来源：
JOURNAL OF APPROXIMATION THEORY | 2014年 / 179卷
基金：
奥地利科学基金会;
关键词：
Korkin-Zolotarev theorem; de Branges spaces; Martin function; Widom domains; Approximation by entire functions; Canonical systems; Spectral theory; ORTHOGONAL POLYNOMIALS; THEOREM;
D O I：
10.1016/j.jat.2013.11.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We generalize the Korkin-Zolotarev theorem to the case of entire functions having the smallest L-1 norm on a system of intervals E. If C \ 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. (C) 2013 Elsevier Inc. All rights reserved.
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页码：63 / 93
页数：31
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