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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Liouville numbers, Rajchman measures, and small Cantor sets


Author: Christian E. Bluhm
Journal: Proc. Amer. Math. Soc. 128 (2000), 2637-2640
MSC (1991): Primary 42A38; Secondary 28A80
Published electronically: February 28, 2000
MathSciNet review: 1657762
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Abstract:

We show that the set of Liouville numbers carries a positive measure whose Fourier transform vanishes at infinity. The proof is based on a new construction of a Cantor set of Hausdorff dimension zero supporting such a measure.


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Additional Information

Christian E. Bluhm
Affiliation: Department of Mathematics, University of Greifswald, Jahnstrasse 15a, D-17487 Greifswald, Germany
Email: bluhm@rz.uni-greifswald.de

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05276-X
PII: S 0002-9939(00)05276-X
Keywords: Liouville numbers, Rajchman measure, Cantor set
Received by editor(s): September 1, 1998
Received by editor(s) in revised form: October 19, 1998
Published electronically: February 28, 2000
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society