Best approximation by «angle» and the absolute Cesaro summability of double Fourier series - Bitimkhan, S.; Mekesh, O. (Karagandy University of the name of acad. E.A. Buketov, 2023)
This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact th a t 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 th a t gives a sufficient condition proves the conditions th a t 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.
«Бурышпен» ең жақсы жуықтау және екі еселі Фурье қатарының Чезаро бойынша абсолютті косындылануы
Наилучшее приближение «углом» и абсолютная суммируемость по Чезаро двойных рядов Фурье
Keywords: trigonometric series; Fourier series; Lebesgue space; best approximation by «angle»; absolute summability of the series