On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions
The sharp Jackson–Stechkin inequalities are received, in which a special module of continuity Ωem(f;t) determined by Steklov’s function is used instead the usual modulus of continuity of mth order ωm(f;t). Such generalized modulus of continuity of mth order were introduced by V.A. Abilov and F.V. Ab...
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Yaroslavl State University
2015-02-01
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| Series: | Modelirovanie i Analiz Informacionnyh Sistem |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/236 |
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doaj-e89c41b573dd47ff90be227e2fe8087b2021-07-29T08:15:19ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172015-02-0122112714310.18255/1818-1015-2015-1-127-143229On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of FunctionsK. Tukhliev0Khujand State UniversityThe sharp Jackson–Stechkin inequalities are received, in which a special module of continuity Ωem(f;t) determined by Steklov’s function is used instead the usual modulus of continuity of mth order ωm(f;t). Such generalized modulus of continuity of mth order were introduced by V.A. Abilov and F.V. Abilova. The introduced modulus of continuity found their application in the theory of polynomial approximation in Hilbert space in the works by M.Sh. Shabozov and G.A. Yusupov, S.B. Vakarchuk and V.I. Zabutnaya and others. While continuing and developing these direction for some classes of functions defined by modulus of continuity, the new values of n-widths in the Hilbert space L₂were found.https://www.mais-journal.ru/jour/article/view/236best polynomial approximationsteklov operatormodulus of continuitygeneralized modulus of continuityn-widths |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
K. Tukhliev |
| spellingShingle |
K. Tukhliev On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions Modelirovanie i Analiz Informacionnyh Sistem best polynomial approximation steklov operator modulus of continuity generalized modulus of continuity n-widths |
| author_facet |
K. Tukhliev |
| author_sort |
K. Tukhliev |
| title |
On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions |
| title_short |
On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions |
| title_full |
On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions |
| title_fullStr |
On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions |
| title_full_unstemmed |
On the Approximation of Periodic Functions in L2 and the Values of the Widths of Certain Classes of Functions |
| title_sort |
on the approximation of periodic functions in l2 and the values of the widths of certain classes of functions |
| publisher |
Yaroslavl State University |
| series |
Modelirovanie i Analiz Informacionnyh Sistem |
| issn |
1818-1015 2313-5417 |
| publishDate |
2015-02-01 |
| description |
The sharp Jackson–Stechkin inequalities are received, in which a special module of continuity Ωem(f;t) determined by Steklov’s function is used instead the usual modulus of continuity of mth order ωm(f;t). Such generalized modulus of continuity of mth order were introduced by V.A. Abilov and F.V. Abilova. The introduced modulus of continuity found their application in the theory of polynomial approximation in Hilbert space in the works by M.Sh. Shabozov and G.A. Yusupov, S.B. Vakarchuk and V.I. Zabutnaya and others. While continuing and developing these direction for some classes of functions defined by modulus of continuity, the new values of n-widths in the Hilbert space L₂were found. |
| topic |
best polynomial approximation steklov operator modulus of continuity generalized modulus of continuity n-widths |
| url |
https://www.mais-journal.ru/jour/article/view/236 |
| work_keys_str_mv |
AT ktukhliev ontheapproximationofperiodicfunctionsinl2andthevaluesofthewidthsofcertainclassesoffunctions |
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1721256630701522944 |