On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals - Yessenbayeva, G.A.; Yesbayev, A.N.; Syzdykova, N.K.; Smirnova, M.A. (Karagandy University of the name of acad. E.A. Buketov, 2023)
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.
Функцияларды тригонометриялық көпмүшелер арқылы жуықтау және гармониялық интервалдарға қатысты функциялар кластарының үйiрлерiнiң қасиеттерi туралы
О приближении функций тригонометрическими полиномами и свойствах семейств классов функций по гармоническим интервалам
Keywords: harmonic interval; spectrum; the best approximation of a function by trigonometric polynomials with a spectrum of harmonic intervals; Dirichlet kernel; family of function classes