Notes on the Theory of Series (XVIII): on the Convergence of Fourier Series

Abstract

1. In this note we give first our proof of a theorem (Theorem 1) which we stated in Note XIII. We then prove a new theorem (Theorem 2) which leads to another proof of the main theorem of Note XVII.The first of these theorems requires some preliminary explanations. We are concerned with an integrable function f (θ) with the period 2π. We writebeing the complex Fourier series of f (θ).