On $L^1$ extremal problem for entire functions

Details On $L^1$ extremal problem for entire functions On $L^1$ extremal problem for entire functions

2012-04-20

arxiv.org/abs/1204.4620v1

Mathematics

Classical Analysis and ODEs

Proves of theorems presented on a conference HCAA 2012, Tenerife, March 5-9, 2012

Scientific paper

We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest $L^1$ norm on a system of intervals $E$. If $\bbC\setminus E$ 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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