On Gruber’s problem concerning uniform distribution on the sphere
✍ Scribed by Aljoša Volčič
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 155 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0003-889X
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📜 SIMILAR VOLUMES
A famous inequality of Erdös and Turán estimates the discrepancy \(\Delta\) of a finite sequence of real numbers by the quantity \(B=\min _{K} K^{-1}+\sum_{k=1}^{K-1}\left|\alpha_{k}\right| / k\), where the \(\alpha_{k}\) are the Fourier coefficients. We investigate how bad this estimate can be. We
The distribution δ (k) (ra) concentrated on the sphere O a with ra = 0 is defined as Taking the Fourier transform of the distribution and the integral representation of the Bessel function, we obtain asymptotic expansions of δ (k) (ra) for k = 0, 1, 2, . . . in terms of △ j δ(x 1 , . . . , x n ), i