On a tauberian theorem for the L1-convergence of Fourier sine series
Abstract
In a recent Tauberian theorem of Stanojevic [3] for the L1-convergence of Fourier series, the notion of asymptotically even sequences is introduced. These conditions are satisfied if the Fourier coefficients {f(n)} are even (f(-n) =f(n)), a case formally equivalent to cosine Fourier series. This paper applies the Tauberian method of Stanojevic [3] separately to cosine and sine Fourier series and shows that the notion of asymptotic evenness can be circumvented in each case. © 1983 American Mathematical Society.
Document Type
Article
DOI
https://doi.org/10.1090/S0002-9939-1983-0691274-0
Keywords
L -convergence of Fourier series 1
Publication Date
1-1-1983
Recommended Citation
Bray, William O. "On a Tauberian theorem for the ��¹-convergence of Fourier sine series." Proceedings of the American Mathematical Society 88, no. 1 (1983): 34-38.
Journal Title
Proceedings of the American Mathematical Society
