Geodesic
On the approximation of entire functions by trigonometric polynomials
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 97-100.

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Let a set $B$ have the following properties: if $z\in B$, then $z\pm2\pi\in B$ and the intersection of $B$ and the strip $0\le\operatorname{Re}x\le\pi$ is a closed and bounded set. In this paper we study the approximation of a continuous on $B$ and $2\pi$-periodic function $f(z)$ by trigonometric polynomials $T_n(z)$. We establish the necessary and sufficient conditions for the function $f(z)$ to be entire and specify a formula for calculating its order. In addition, we describe some metric properties of periodic sets in a plane.
Keywords: trigonometric polynomials, entire function, order of entire function, Fekete numbers. 
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     author = {E. G. Kir'yatskii},
     title = {On the approximation of entire functions by trigonometric polynomials},
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E. G. Kir'yatskii. On the approximation of entire functions by trigonometric polynomials. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 97-100. http://geodesic.mathdoc.fr/item/IVM_2010_2_a9/

[1] Uolsh Dzh. L., Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, In. lit., M., 1961, 508 pp. | MR

[2] Fekete M., “Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten”, Math. Zeitschrift., 17 (1923), 228–249 | DOI | MR | Zbl

[3] Naftalevich A. G., “O priblizhenii analiticheskikh funktsii algebraicheskimi mnogochlenami”, Litovskii matem. sb., 9:3 (1969), 577–588 | Zbl