ON THE INTERPOLATION IN SOME CLASSES OF HOLOMORPHIC IN THE UNIT DISK FUNCTIONS.

There is considered an interpolation problem f(λ_n) = b_n in the class of holomorphic in the unit disk U(0; 1) = {z ε C: |z| < 1} functions of finite η-type, i.e such that... where η: [1;+∞) → [0;+∞) is an increasing convex function with respect to ln t and ln t = o (η(t)) (t → +∞). There were received sufficient conditions of the interpolation problem solvability in terms of the counting functions.... Earlier, in 2004, necessary conditions were obtained (Ukr. Math. J., 56 (2004), №3) in these terms. For the moderate growth of f (when the majorant η = ψ satisfies the condition ψ (2x) = O (ψ (x)), x → +∞) that problem was solved in J. Math. Anal. Appl., 414 (2014), №1. In this paper, we remove any restrictions on the growth of η and construct an interpolation function f such that... [ABSTRACT FROM AUTHOR]