Abstract
Let a set B have the following properties: if z ∈ B, then z ± 2π ∈ B and the intersection of B with the vertical strip 0 ≤ Re x ≤ π is a closed and bounded set. In this paper we study the approximation of a continuous on B and 2π-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.
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References
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Original Russian Text © E.G. Kir’yatskii, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 2, pp. 97–100.
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Kir’yatskii, E.G. On the approximation of entire functions by trigonometric polynomials. Russ Math. 54, 84–86 (2010). https://doi.org/10.3103/S1066369X10020106
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DOI: https://doi.org/10.3103/S1066369X10020106