Magnified curves on a flat torus, determination of almost periodic functions, and the Riemann-Lebesgue lemma
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- by Robert S. Strichartz PDF
- Proc. Amer. Math. Soc. 107 (1989), 755-759 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 755-759
- MSC: Primary 42A75
- DOI: https://doi.org/10.1090/S0002-9939-1989-0994791-4
- MathSciNet review: 994791