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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- Yves Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87–99 (French). MR 227697, DOI https://doi.org/10.4064/sm-30-1-87-99
- I. Glicksberg, Fourier-Stieltjes transforms with small supports, Illinois J. Math. 9 (1965), 418–427. MR 192280
- N. I. Ahiezer, Lekcii po Teorii Approksimacii, OGIZ, Moscow-Leningrad,], 1947 (Russian). MR 0025598
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42.52
Retrieve articles in all journals with MSC: 42.52
Additional Information
Keywords:
Fourier-Stieltjes coefficients,
convolution,
absolutely continuous measure,
F. and M. Riesz Theorem
Article copyright:
© Copyright 1970
American Mathematical Society