One problem of extremal functional interpolation and the Favard constants

For an extremal functional interpolation problem first considered by Yu.N. Subbotin, the explicit form of the extremal interpolation constants is calculated in terms of the Favard constants in the spaces $L_p$, $p=1,3/2,2$. Simple efficient recurrence formulas are obtained to calculate the Favard constants, and formulas for calculating these constants in terms of the Euler numbers are also given.