Tauberian theorems for Nörlund summability and their application to the convergence of Fourier series
The author obtains Tauberian theorems for Nörlund summability methods in Section 3. His results generalize well-known Tauberian theorems. In Section 4, the author presents a corrected proof of a one-sided Tauberian theorem for Nörlund summability which was stated by \textit{K. S. K. Iyengar} [Proc. Indian Acad. Sci., Sect. A 18, 113--120 (1943; Zbl 0060.18501)] and defectively proved by \textit{O. P. Varshney} [Tohoku Math. J. (2) 16, 105--110 (1964; Zbl 0133.01302)] and establishes corresponding \(O\)-Tauberian theorems. In Section 5, the author studies the relationship between the Tauberian theorems given in Sections 3 and 4. In Section 6, the author applies his results to the convergence of Fourier series.
scientific article; zbMATH DE number 6568434