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| ≤ ∆ 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 coeffcient A0 is an entire function from the mentioned class.

Keywords

• interpolation problem
• entire function
• solution of differential equation