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. 
@article{IVM_2010_2_a9,
     author = {E. G. Kir'yatskii},
     title = {On the approximation of entire functions by trigonometric polynomials},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {97--100},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_2_a9/}
}
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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/