Abstract

Abstract. We prove that no ball admits a non-harmonic orthogonal basis of exponentials. We use a combinatorial result, originally studied by Erdős, which says that the number of distances determined by n points in Rd is at least Cdn 1 d +ǫd, ǫd> 0. Introduction and statement of results Fourier bases. Let D be a domain in R d, i.e., D is a Lebesgue measurable subset of R d with finite non-zero Lebesgue measure. We say that D is a spectral set if L 2 (D) has orthogonal basis of the form EΛ = {e 2πix·λ}

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