Best approximation by «angle» and the absolute Cesàro summability of double Fourier series
«Бұрышпен» ең жақсы жуықтау және екi еселi Фурье қатарының Чезаро бойынша абсолюттi қосындылануы
Наилучшее приближение «углом» и абсолютная суммируемость по Чезаро двойных рядов Фурье
Bitimkhan S. Mekesh O.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#112Issue 456 - 65 pp.
This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector index absolute summation method was obtained in terms of the best approximation by «angle» of the functions from Lebesgue space. The theorem that gives a sufficient condition proves the conditions that are sufficient in different cases, which may depend on the parameters. From this proved theorem, a sufficient condition on the term mixed smoothness modulus of the function from Lebesgue space, which is easily obtained by a well-known inequality, is also presented.
absolute summability of the series , best approximation by «angle» , Fourier series , Lebesgue space , trigonometric series
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
S. Seifullin Kazakh Agro-Technical Research University, Astana, Kazakhstan
L.N. Gumilyov Eurasian National University
S. Seifullin Kazakh Agro-Technical Research University
10 лет помогаем публиковать статьи Международный издатель
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