Arithmetic properties of sparse subsets of $\mathbb{Z}^n$
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Publication:4989355
zbMath1464.42004arXiv1602.01634MaRDI QIDQ4989355
Publication date: 25 May 2021
Full work available at URL: https://arxiv.org/abs/1602.01634
parallelogramdiscrete Fourier transformHausdorff dimensionarithmetic progressionFourier dimensionFourier-Stieltjes transform
Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) (43A46) Fourier series and coefficients in several variables (42B05) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Arithmetic progressions (11B25) Hausdorff and packing measures (28A78)
Cites Work
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- Finite configurations in sparse sets
- On the sharpness of Mockenhaupt's restriction theorem
- Arithmetic progressions in Salem-type subsets of the integers
- Arithmetic progressions in sets of fractional dimension
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- A relative Szemerédi theorem
- On singular monotonic functions whose spectrum has a given Hausdorff dimension
- A Class of Random Cantor Measures, with Applications
- Salem Sets with No Arithmetic Progressions
- On some properties of symmetrical perfect sets
- Salem sets and restriction properties of Fourier transforms
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