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 ( c_1 > 0 ) ( z, | z | < 1 ): | f( z ) | ( c_1 η ( c_1 1 - | z | ) ). 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 → ∞.