On the Properties of Wiener-Lévy Functions

Abstract: This thesis concerns the Wiener algebra of periodic functions with absolutely convergent Fourier series, and the "Wiener-Lévy functions", meaning functions that preserve absolute convergence of Fourier series under composition. Results regarding the properties of functions in the Wiener algebra are established, as well as properties of Wiener-Lévy functions. By the Wiener-Lévy Theorem, analyticity is a sufficient condition for a function to be a Wiener-Lévy function, and in this paper, we find the necessary condition of being real analytic in the real and imaginary variable, separately.