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Proceedings of the American Mathematical Society

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Fourier-Stieltjes transforms tending to zero

Author: Lawrence J. Wallen
Journal: Proc. Amer. Math. Soc. 24 (1970), 651-652
MSC: Primary 42.52
MathSciNet review: 0256079
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Abstract: Let $ \mu $ be a Borel measure on the circle, $ \hat \mu $ its Fourier transform. It is shown that a certain thinness condition on the positive part of the support of $ \hat \mu $ forces a power of $ \mu $ (in the sense of convolution) to be absolutely continuous.

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  • [1] Y. Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87-99. MR 37 #3281. MR 0227697 (37:3281)
  • [2] I. Glicksberg, Fourier-Stieltjes transforms with small supports, Illinois J. Math. 9 (1965), 418-427. MR 33 #506. MR 0192280 (33:506)
  • [3] N. I. Ahieser, Lectures on the theory of approximation, OGIZ, Moscow, 1947; English transl., Ungar, New York, 1956. MR 10, 33; MR 20 #1872. MR 0025598 (10:33b)

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Keywords: Fourier-Stieltjes coefficients, convolution, absolutely continuous measure, F. and M. Riesz Theorem
Article copyright: © Copyright 1970 American Mathematical Society

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