On the L1L1 extremal problem for entire functions

We generalize the Korkin–Zolotarev theorem to the case of entire functions having the smallest L1L1 norm on a system of intervals EE. If C∖EC∖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.