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Proceedings of the American Mathematical Society

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

 

 

Fourier-Stieltjes transforms tending to zero


Author: Lawrence J. Wallen
Journal: Proc. Amer. Math. Soc. 24 (1970), 651-652
MSC: Primary 42.52
DOI: https://doi.org/10.1090/S0002-9939-1970-0256079-4
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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DOI: https://doi.org/10.1090/S0002-9939-1970-0256079-4
Keywords: Fourier-Stieltjes coefficients, convolution, absolutely continuous measure, F. and M. Riesz Theorem
Article copyright: © Copyright 1970 American Mathematical Society