Approximation of classes of Poisson integrals by Fejer means
The work is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series. The simplest example of a linear approximation of periodic functions is the approximation of funct...
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| Format: | Article |
| Language: | English |
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V.N. Karazin Kharkiv National University Publishing
2023-05-01
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| Series: | Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika |
| Subjects: | |
| Online Access: | https://periodicals.karazin.ua/mech_math/article/view/21179 |
| _version_ | 1797682109256564736 |
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| author | O. G. Rovenska |
| author_facet | O. G. Rovenska |
| author_sort | O. G. Rovenska |
| collection | DOAJ |
| description | The work is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series.
The simplest example of a linear approximation of periodic functions is the approximation of functions by partial sums of their Fourier series. However, the sequences of partial Fourier sums are not uniformly convergent over the class of continuous periodic functions. Therefore, a many studies is devoted to the research of the approximative properties of approximation methods, which are generated by transformations of the partial sums of Fourier series and allow us to construct sequences of trigonometrical polynomials that would be uniformly convergent for the whole class of continuous functions. Particularly, Fejer means have been widely studied in the last time. One of the important problems in this field is the study of asymptotic behavior of the upper bounds over a fixed classes of functions of deviations of the trigonometric polynomials.
The aim of the work systematizes known results related to the approximation of classes of Poisson integrals of continuous functions by arithmetic means of Fourier sums, and presents new facts obtained for particular cases.
The asymptotic behavior of the upper bounds on classes of Poisson integrals of periodic functions of the real variable of deviations of linear means of Fourier series, which are defined by applying the Fejer summation method is studied. The mentioned classes consist of analytic functions of a real variable, which are narrowing of bounded harmonic in unit disc functions of complex variable. In the work, asymptotic equalities for the upper bounds of deviations of Fejer means on classes of Poisson integrals were obtained. |
| first_indexed | 2024-03-11T23:54:48Z |
| format | Article |
| id | doaj.art-16694a9a4caa44e1bb2c6bcfa8a7bf12 |
| institution | Directory Open Access Journal |
| issn | 2221-5646 2523-4641 |
| language | English |
| last_indexed | 2024-03-11T23:54:48Z |
| publishDate | 2023-05-01 |
| publisher | V.N. Karazin Kharkiv National University Publishing |
| record_format | Article |
| series | Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika |
| spelling | doaj.art-16694a9a4caa44e1bb2c6bcfa8a7bf122023-09-18T16:52:38ZengV.N. Karazin Kharkiv National University PublishingVisnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika2221-56462523-46412023-05-019741210.26565/2221-5646-2023-97-0121179Approximation of classes of Poisson integrals by Fejer meansO. G. Rovenska0Donbass State Engineering AcademyThe work is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series. The simplest example of a linear approximation of periodic functions is the approximation of functions by partial sums of their Fourier series. However, the sequences of partial Fourier sums are not uniformly convergent over the class of continuous periodic functions. Therefore, a many studies is devoted to the research of the approximative properties of approximation methods, which are generated by transformations of the partial sums of Fourier series and allow us to construct sequences of trigonometrical polynomials that would be uniformly convergent for the whole class of continuous functions. Particularly, Fejer means have been widely studied in the last time. One of the important problems in this field is the study of asymptotic behavior of the upper bounds over a fixed classes of functions of deviations of the trigonometric polynomials. The aim of the work systematizes known results related to the approximation of classes of Poisson integrals of continuous functions by arithmetic means of Fourier sums, and presents new facts obtained for particular cases. The asymptotic behavior of the upper bounds on classes of Poisson integrals of periodic functions of the real variable of deviations of linear means of Fourier series, which are defined by applying the Fejer summation method is studied. The mentioned classes consist of analytic functions of a real variable, which are narrowing of bounded harmonic in unit disc functions of complex variable. In the work, asymptotic equalities for the upper bounds of deviations of Fejer means on classes of Poisson integrals were obtained.https://periodicals.karazin.ua/mech_math/article/view/21179poisson integral; fejer mean; asymptotic equality |
| spellingShingle | O. G. Rovenska Approximation of classes of Poisson integrals by Fejer means Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika poisson integral; fejer mean; asymptotic equality |
| title | Approximation of classes of Poisson integrals by Fejer means |
| title_full | Approximation of classes of Poisson integrals by Fejer means |
| title_fullStr | Approximation of classes of Poisson integrals by Fejer means |
| title_full_unstemmed | Approximation of classes of Poisson integrals by Fejer means |
| title_short | Approximation of classes of Poisson integrals by Fejer means |
| title_sort | approximation of classes of poisson integrals by fejer means |
| topic | poisson integral; fejer mean; asymptotic equality |
| url | https://periodicals.karazin.ua/mech_math/article/view/21179 |
| work_keys_str_mv | AT ogrovenska approximationofclassesofpoissonintegralsbyfejermeans |