Geodesic
Constructive description of a class of periodic functions on the real line
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 36-46.

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With a help of some family ${\mathcal H}$ of convex nondecreasing functions on $[0, \infty)$ we define the space $G({\mathcal H})$ of $2 \pi$-periodic infinitely differentiable functions on the real line with given estimates for all derivatives. A description of the space $G({\mathcal H})$ is obtained in terms of the best trigonometric approximations and the rate of decrease of the Fourier coefficients. There are given families ${\mathcal H}$ for which functions from $G({\mathcal H})$ can be extended to analytic functions in the horizontal strip of the complex plane. An internal description of the space of such extensions is obtained. Examples of a family of convex functions ${\mathcal H}$ are given.
Keywords: Fourier series, approximation by trigonometric polynomials.
Mots-clés : Fourier coefficients 
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I. Kh. Musin. Constructive description of a class of periodic functions on the real line. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 36-46. http://geodesic.mathdoc.fr/item/IVM_2023_2_a2/

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