Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)$.

References [Enhancements On Off] (What's this?)

  • [1] R. E. Edwards, Fourier Series, Vol. 1, Springer-Verlag, New York and Heidelberg, 1979. MR 545506 (80j:42001)
  • [2] G. H. Hardy and W. Rogosinski, Fourier series, Cambridge Univ. Press, New York, 1965. MR 0010206 (5:261d)
  • [3] M. Taibleson, Fourier coefficients of functions of bounded variation, Proc. Amer. Math. Soc. 18 (1967), 766. MR 0212477 (35:3348)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A16

Retrieve articles in all journals with MSC: 42A16

Additional Information

Keywords: Fourier coefficients
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society