On interpolation problem with derivative in the space of entire functions with fast-growing interpolation knots. (English) Zbl 1425.30037
Summary: In the paper there are obtained the conditions on a sequence \((b_{k,1}; b_{k,2}),\ k \in{\mathbb N},\) such that the interpolation problem \(g(\lambda _{k} ) = b_{k,1} ,\ {g}'(\lambda _{k} ) = b_{k,2} \) has a unique solution in a subspace of entire functions \( g \) that satisfy the condition \(\ln M_g (r)\le c_1\exp\left(N(r)+N(\rho_1 r)\right)\), where \(\vert \lambda_{k}/\lambda_{k + 1}\vert \le \Delta \le1\), and \(N(r)\) is Nevanlinna counting function of the sequence (\(\lambda_k\)). These results have been applied to the description of the solutions of the differential equation \(f''+a_0 f=0\) with a coefficient \(a_0\) from the some space of entire functions.
MSC:
| 30E05 | Moment problems and interpolation problems in the complex plane |
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
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