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Статья

Approximation by Entire Functions on a Countable Set of Continua

Vestnik St. Petersburg University: Mathematics. 2020. Vol. 53. P. 329-335.
Silvanovich O. V., Shirokov N. A.

The problem of approximation by entire functions of exponential type defined on a countable set E of continua GnE = ⋃n∈ZGn⋃n∈ZGn is considered in this paper. It is assumed that all Gn are pairwise disjoint and are situated near the real axis. It is also assumed that all Gn are commensurable in a sense and have uniformly smooth boundaries. A function f is defined independently on each Gn and is bounded on E and f (r) has a module of continuity ω which satisfies the condition (1). An entire function Fσ of exponential type ≤σ is then constructed so that the following estimate of approximation of the function f   by functions Fσ is valid