Universal Spectra , Universal Tiling Sets and Thespectral Set


A subset of R d with nite positive Lebesgue measure is called a spectral set if there exists a subset R such that E := n e i2h;xi : 2 o form an orthogonal basis of L 2 ((). The set is called a spectrum of the set. The Spectral Set Conjecture states that is a spectral set if and only if tiles R d by translation. In this paper we prove the Spectral Set… (More)