Abstract

Fourier series form a corner stone of analysis; it allows the expansion of a complex valued functions defined on the unit interval in the orthogonal basis of integer frequency exponentials. A simple rescaling argument shows that by splitting the integers into even and odds, we obtain orthogonal bases for functions defined on the first, respectively the second half of the unit interval.

We shall generalize this curiosity in one and higher dimensions and thereby achieve novel results on cube tilings and the so-called Chebotarev theorem on Fourier minors. The talk is designed to be accessible by undergraduate students.