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

Iranian Journal of Numerical Analysis and Optimization

دوره 12، شماره 1 - شماره پیاپی 21، خرداد 2022، صفحه 131-144   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.70074.1028

نویسنده

I. Sheparovych^*

Department of Physics, Mathematics, Economy and Innovative Technologies, Ivan Franko State Pedagogical Institute of Drohobych, Drohobych, Ukraine.

چکیده

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 coeffcient A0 is an entire function from the mentioned class.

کلیدواژه‌ها

Interpolation problem؛ Entire function؛ Solution of differential equation

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