On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals
Функцияларды тригонометриялық көпмүшелер арқылы жуықтау және гармониялық интервалдарға қатысты функциялар кластарының үйірлерінің қасиеттері туралы
О приближении функций тригонометрическими полиномами и свойствах семейств классов функций по гармоническим интервалам
Yessenbayeva G.A. Yesbayev A.N. Syzdykova N.K. Smirnova M.A.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#111Issue 3181 - 190 pp.
The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. In this paper, the spectrum consists of harmonic intervals. Devices, various processes, perception of the senses have a limited range. In the mathematical modeling of numerous practical problems and in the further study of such mathematical models, it is sufficient to find a solution in this range. It is possible to study such models to some extent with the help of harmonic intervals. To prove the main theorem, an auxiliary lemma was proved, and elements of the theory of approximations with respect to harmonic intervals were used. For the constructed families of function classes associated with the best approximations by trigonometric polynomials with a spectrum of harmonic intervals, their relationship with classical Besov spaces is shown.
Dirichlet kernel , family of function classes , harmonic interval , spectrum , the best approximation of a function by trigonometric polynomials with a spectrum of harmonic intervals
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Karaganda University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
Nazarbayev Intellectual School of Astana, Astana, Kazakhstan
Karaganda University of the name of academician E.A. Buketov
Nazarbayev Intellectual School of Astana
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