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

 

Magnified curves on a flat torus, determination of almost periodic functions, and the Riemann-Lebesgue lemma


Author: Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 107 (1989), 755-759
MSC: Primary 42A75
MathSciNet review: 994791
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Abstract: Simple arguments, based on the Riemann-Lebesgue Lemma, are given to show that for a large class of curves $ \gamma $ in $ {{\mathbf{R}}^n}$, any almost periodic function is determined by its restriction to large dilates of $ \gamma $. Specializing to periodic functions, this means that magnified images of $ \gamma $ on a flat torus tend to uniformly dense scribbles.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0994791-4
PII: S 0002-9939(1989)0994791-4
Article copyright: © Copyright 1989 American Mathematical Society