Title

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

Journal Title

Proceedings of the American Mathematical Society

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