A Additional Preliminaries

Given a T -periodic function f ( x), its Fourier series representation is a decomposition into a sum of Fourier basis functions. Polynomial images are simpler to sketch. Fourier spectra are appropriately bounded as described in Assumption B.1. Lemma B.2 (The Image Norm is Bounded) . The statement follows from Assumption B.1 and an application of Parseval's theorem. Parseval's theorem, we have that, Z We will use Fourier analysis for our argument.