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ON THE APPROXIMATION OF UNIFORM ALMOST PERIODIC FUNCTIONS BY CERTAIN SUMS AND INTEGRALS

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Talbakov F.M.

 

The paper investigates some issues of approximation of almost-periodic Bohr functions from partial sums of the Fourier series and the Marcinkevich averages, when the Fourier exponents (the spectrum of the function) of the functions under consideration have a limit point at infinity. The question of the deviation of a given function f(x) from its partial sums of the Fourier series is investigated, depending on the rate of tendency to zero of the magnitude

of the best approximation by a trigonometric polynomial of bounded degree. Here, when determining the Fourier coefficients, instead of the function under consideration, some arbitrary, real, continuous function ,  is taken, which in a given interval is equal to one, and in other cases is zero. Then, similarly, the upper estimate of the deviation of the almost-periodic in the sense of the Bohr function by the Marcinkevich averages is established.

 

Keywords: uniform almost-periodic functions, Fourier series, function spectrum, Fourier coefficients, limit point at infinity, Marcinkevich averages, trigonometric polynomial, best approximation.

 

Information about the author

 

Talbakov Farkhodjon Makhmadshoevich - Tajik State Pedagogical University named after. S. Aini,

Candidate of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Geometry and Higher Mathematics. 

Address: 734003, Dushanbe, Republic of Tajikistan, Rudaki, 121. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..

 

REVIEWER: Abdukarimov M.F., Doctor of Physical and Mathematical Sciences,  Associate Professor

 

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Article received: 25.12.2023

Approved after review: 13.01.2024

Accepted for publication: 07.03.2024

 

   
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