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On a Tauberian theorem for the $ L\sp{1}$-convergence of Fourier sine series

Author: William O. Bray
Journal: Proc. Amer. Math. Soc. 88 (1983), 34-38
MSC: Primary 42A20
MathSciNet review: 691274
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Abstract: In a recent Tauberian theorem of Stanojević [3] for the $ {L^1}$-convergence of Fourier series, the notion of asymptotically even sequences is introduced. These conditions are satisfied if the Fourier coefficients $ \{ \hat f(n)\} $ are even $ (\hat f( - n) = \hat f(n))$, a case formally equivalent to cosine Fourier series. This paper applies the Tauberian method of Stanojević [3] separately to cosine and sine Fourier series and shows that the notion of asymptotic evenness can be circumvented in each case.

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Keywords: $ {L^1}$-convergence of Fourier series
Article copyright: © Copyright 1983 American Mathematical Society

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