On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness
| Autor: | Mikhail K. Potapov, Nimete Sh. Berisha, Marjan Dema, Faton M. Berisha |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Smoothness (probability theory) Series (mathematics) Article Subject Applied Mathematics lcsh:Mathematics 010102 general mathematics Order (ring theory) Type (model theory) lcsh:QA1-939 01 natural sciences Moduli 010101 applied mathematics Monotone polygon Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics 42A10 42A16 0101 mathematics Lacunary function Fourier series Analysis Mathematics |
| Zdroj: | Abstract and Applied Analysis, Vol 2017 (2017) Abstr. Appl. Anal. |
| ISSN: | 1687-0409 1085-3375 |
| Popis: | In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities. Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:1208.6123 |
| Databáze: | OpenAIRE |
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