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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Coefficients de Fourier de fonctions à variation bornée


Author: Jie Wu
Journal: Proc. Amer. Math. Soc. 117 (1993), 689-690
MSC: Primary 42A16
MathSciNet review: 1150658
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Abstract: Let $ f:\mathbb{R} \to \mathbb{C}$ be a function of period $ 2\pi $ and of bounded variation on $ [0,2\pi ]$ with the total variation $ V(f)$. Its Fourier coefficients are denoted by $ \hat f(n)$. In this short note, we give a very simple proof of the known result $ \vert\hat f(n)\vert \leqslant V(f)/2\pi \vert n\vert\;(n \in \mathbb{Z},\;n \ne 0)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1150658-3
PII: S 0002-9939(1993)1150658-3
Keywords: Fourier coefficients
Article copyright: © Copyright 1993 American Mathematical Society