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Planar Fourier transforms and Diophantine approximation


Author: R. Kaufman
Journal: Proc. Amer. Math. Soc. 40 (1973), 199-204
MSC: Primary 42A92
DOI: https://doi.org/10.1090/S0002-9939-1973-0320626-7
MathSciNet review: 0320626
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Abstract: The radial behavior of its Fourier-Stieltjes transform in $ {R^2}$ is related to the modulus of continuity of a measure; in certain cases the Hausdorff dimension of an exceptional set of lines can be estimated. Converse results use the theory of Diophantine approximation established by Besicovitch and Jarník.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0320626-7
Keywords: Fourier-Stieltjes transform, Hausdorff dimension, $ {J_0}$, Diophantine approximation
Article copyright: © Copyright 1973 American Mathematical Society

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