On Interpolation Sequences of One Class of Functions Analytic in the Unit Disk - Vynnyts’kyi, B. V.; Sheparovych, I. B. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We establish a criterion for the existence of a solution of the interpolation problem f(λ n ) = b n in the class of functions f analytic in the unit disk and satisfying the relation $$\left( {\exists {τ }_{1} \in \left( {0;1} \right)} \right)\;\left( {\exists c_1 >0} \right)\;\left( {\forall z,\left| z \right| < 1} \right):\;\left| {f\left( z \right)} \right| \leqslant \exp \left( {c_1 γ ^{{τ }_{1} } \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right),$$ where γ: [1; +∞) → (0; +∞) is an increasing function such that the function lnγ(t) is convex with respect to lnt on the interval [1; +∞) and lnt = o(lnγ(t)), t → ∞.