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

 

On the magnitude of Fourier coefficients


Authors: Michael Schramm and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 85 (1982), 407-410
MSC: Primary 42A16; Secondary 26A45
MathSciNet review: 656113
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Abstract: If $ f$ is a function on $ {R^1}$ of $ \Lambda $-bounded variation and period $ 2\pi $, then its $ n$th Fourier coefficient $ \hat f(n) = O(1/\Sigma _1^n1/{\lambda _j})$ and its integral modulus of continuity $ {\omega _1}(f;\delta ) = O(1/\Sigma _1^{[1/\delta ]}1/{\lambda _j})$. The result on $ \hat f(n)$ is best possible in a sense. These results can be extended to certain other classes of functions of generalized variation.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0656113-1
PII: S 0002-9939(1982)0656113-1
Article copyright: © Copyright 1982 American Mathematical Society