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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On certain sums of Fourier-Stieltjes coefficients
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by J. B. Twomey PDF
Trans. Amer. Math. Soc. 280 (1983), 611-621 Request permission

Abstract:

We obtain estimates for certain sums of Fourier-Stieltjes (and hence also Fourier) coefficients of continuous functions $f$ of bounded variation in terms of the modulus of continuity of $f$. As a consequence of one of our results we obtain an improvement on a theorem of Zygmund on the absolute convergence of Fourier series of functions of bounded variation. We also consider absolutely continuous functions and show by examples that a number of the results we obtain are "best possible".
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 280 (1983), 611-621
  • MSC: Primary 42A16; Secondary 42A28
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0716840-X
  • MathSciNet review: 716840