  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.
