Fourier bases and a distance problem of Erd\H os

Details Fourier bases and a distance problem of Erd\H os Fourier bases and a distance problem of Erd\H os

2001-04-08

arxiv.org/abs/math/0104092v1

Math Research Letters Volume 6 (1999) No. 2 pp. 105-128

Mathematics

Classical Analysis and ODEs

Scientific paper

We prove that no ball admits a non-harmonic orthogonal basis of exponentials.
We use a combinatorial result, originally studied by Erd\H os, which says that
the number of distances determined by $n$ points in ${\Bbb R}^d$ is at least
$C_d n^{\frac{1}{d}+\epsilon_d}$, $\epsilon_d>0$.

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