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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the magnitude of Fourier coefficients
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by Michael Schramm and Daniel Waterman PDF
Proc. Amer. Math. Soc. 85 (1982), 407-410 Request permission

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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 407-410
  • MSC: Primary 42A16; Secondary 26A45
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656113-1
  • MathSciNet review: 656113