Multiple interpolation with the fast-growing knots in the class of entire functions and its application

Abstract

The conditions for the sequence of complex numbers (bn,k) are obtained, such that the interpolation problem g(k−1)(λn) = bn,k, k ∈ 1, s, n ∈ N, where |λk/λk+1| ≤ ∆ < 1, has a unique solution in some classes of entire functions g for which Mg(r) ≤ c1 exp ((s − 1)N(r) + N(ρ1r)), where N(r) is the counting function of the sequence (λn), ρ1 ∈ (∆; 1), and c1 > 0. Moreover, these results have been applied to the description of the solution of the differential equation f(s)+A0(z)f = 0 for which (λn) is zero-sequence and the coefficient A0 is an entire function from the mentioned class.