Uma alternativa rigorosa para o ensino das séries de Fourier

Abstract

Fourier series can represent a variety of periodic functions. There is a difference between studying Fourier series and power series, because, respectively, one works as a global process and the other as a local process. And so, in some problems it is not feasible to apply the power series, on the contrary, it is necessary to apply the Fourier series. In this research we present a rigorous alternative for teaching Fourier series on different orthogonal decompositions of a function, relating them mathematically in certain metric spaces that are called Discrete Fourier Transform and Fourier Transform, so that the interested reader can continue your studies under the scope you prefer, be it theoretical or practical.