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

The conditions for the sequence of complex numbers (bn,k) are obtained, such that the interpolation problem g(k-۱)(λn) = bn,k, k ∈ ۱, s, n ∈ N, where |λk/λk+۱| ≤ ∆ < ۱, has a unique solution in some classes of entire functions g for which Mg(r) ≤ c۱ exp ((s - ۱)N(r) + N(ρ۱r)), where N(r) is the counting function of the sequence (λn), ρ۱ ∈ (∆; ۱), and c۱ > ۰. Moreover, these results have been applied to the description of the solution of the differential equation f(s) +A۰(z)f = ۰ for which (λn) is zero-sequence and the coeffcient A۰ is an entire function from the mentioned class.

کلیدواژه ها:

Interpolation problem ، Entire function ، Solution of differential equation