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Fourier series with positive coefficients

Authors: J. Marshall Ash, Michael Rains and Stephen Vági
Journal: Proc. Amer. Math. Soc. 101 (1987), 392-393
MSC: Primary 42A32; Secondary 42A16, 43A15
MathSciNet review: 902561
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Abstract: Extending a result of N. Wiener, it is shown that functions on the circle with positive Fourier coefficients that are $ p$th power integrable near $ 0,1 < p \leq 2$, have Fourier coefficients in $ {l^{p'}}$.

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

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  • [2] M. Rains, On functions with nonnegative Fourier transforms, Indian J. Math. 27 (1985), 41-48. MR 852132 (87k:43005)
  • [3] H. S. Shapiro, Majorant problems for Fourier coefficients, Quart. J. Math. Oxford (2) 26 (1975), 9-18. MR 0372515 (51:8722)
  • [4] S. Wainger, A problem of Wiener and the failure of a principle for Fourier series with positive coefficients, Proc. Amer. Math. Soc. 20 (1969), 16-18. MR 0236397 (38:4693)
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Article copyright: © Copyright 1987 American Mathematical Society

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