Interpolation sequences for the class of functions of finite η-type analytic in the unit disk

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 (∃c1 > 0) (∀ z,|z| < 1): |f(z)| ≤ exp(c1η(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 → ∞. © 2004 Springer Science+Business Media, Inc.