Interpolation Sequences for the Class of Functions of Finite η-Type Analytic in the Unit Disk - Vynnyts’kyi, B. V.; Sheparovych, I. B. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We establish conditions 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 such that $$\left( {\exists \;c_1 > 0} \right)\;\left( {\forall z,\;|\;z\;| < 1} \right):\;\;\left| {f\left( z \right)} \right|\;\; \leqslant \;\;\;\exp \left( {c_1 η \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right).$$ Here, η : [1; +∞) → (0; +∞) is an increasing function convex with respect to ln t on the interval [1; +∞) and such that ln t = o(η(t)), t → ∞.