Fourier-Stieltjes transforms tending to zero
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- by Lawrence J. Wallen
- Proc. Amer. Math. Soc. 24 (1970), 651-652
- DOI: https://doi.org/10.1090/S0002-9939-1970-0256079-4
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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.References
- Yves Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87–99 (French). MR 227697, DOI 10.4064/sm-30-1-87-99
- I. Glicksberg, Fourier-Stieltjes transforms with small supports, Illinois J. Math. 9 (1965), 418–427. MR 192280, DOI 10.1215/ijm/1256068144
- N. I. Ahiezer, Lekcii po Teorii Approksimacii, OGIZ, Moscow-Leningrad, 1947 (Russian). MR 0025598
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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