On interpolation problem with derivative in a space of entire functions with fast-growing interpolation knots

Abstract

We obtaine the conditions on a sequence (bhas the unique solution in a subspace of entire functions g satisfying the condition ln M g (r) ≤ c 1 exp (N (r) + N (ρ 1 r)), where |λ k /λ k+1 | ≤ ∆ < 1, and N (r) is the Nevanlinna counting function of the sequence (λ k ). These results have been applied to describe solutions of the differential equation f ′′ + a 0 f = 0 with a coefficient a 0 from the some space of entire functions.