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The dual spectral set conjecture

Authors:	Steen Pedersen

Institution:	Department of Mathematics, Wright State University, Dayton, Ohio 45435

Abstract:	Suppose that $\Lambda=(a\mathbf{Z}+b)\cup(c\mathbf{Z}+d)$ where are real numbers such that $a\neq0$ and $c\neq0.$ The union is not assumed to be disjoint. It is shown that the translates $\Omega+\lambda$ , $\lambda\in\Lambda$ , tile the real line for some bounded measurable set $\Omega$ if and only if the exponentials $e_{\lambda}(x)=e^{i2\pi\lambda x}$ , $\lambda\in\Lambda$ , form an orthogonal basis for some bounded measurable set $\Omega'.$

Keywords:	Fourier basis non-harmonic Fourier series tiling spectral set spectral pair

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