On the boundedness of the partial sums operator for the Fourier series in the function classes families associated with harmonic intervals
Гармоникалық интервалдармен байланысты функциялар кластары үйiрiндегi Фурье қатарының дербес қосындылары операторының шенелгендiгi туралы
Об ограниченности оператора частичных сумм ряда Фурье в семействах классов функций, связанных с гармоническими интервалами
Yessenbayeva G.A. Yessenbayeva G.A. Kasimov A.T. Syzdykova N.K.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#103Issue 3131 - 139 pp.
The article is devoted to the study of some data from the theory of functions approximation by trigonometric polynomials with a spectrum from special sets called harmonic intervals. Due to the limited perception range of devices, the perception range of the senses of the person himself, when studying a mathematical model it is often enough to find an approximation of the object so that the error (noise, interference, distortion) is outside the interval of perception. Harmonic intervals model problems of this kind to some extent. In the article the main components of the approximation theory of functions by trigonometric polynomials with a spectrum from harmonic intervals are presented, the theorem on estimating the best approximation of a function by trigonometric polynomials through the best approximations of a function by trigonometric polynomials with a spectrum from harmonic intervals is proved. Theorems on the boundedness of the partial sums operator for the Fourier series in the function classes families associated with harmonic intervals are considered; such a theorem for the Lorentz space is generalized and proved. The article is mainly aimed at scientific researchers dealing with practical applications of the approximation theory of functions by trigonometric polynomials with a spectrum from special sets.
best approximation of a function by trigonometric polynomials , harmonic interval , interpolation theorem , partial sums operator of the Fourier series for a given function , trigonometric polynomials with a spectrum from harmonic intervals
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Karagandy University of the name of Academician E.A. Buketov, Karaganda, Kazakhstan
Karaganda University of Kazpotrebsoyuz, Karaganda, Kazakhstan
Karaganda Technical University, Karaganda, Kazakhstan
Karagandy University of the name of Academician E.A. Buketov
Karaganda University of Kazpotrebsoyuz
Karaganda Technical University
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