Abstract
This chapter discusses the harmonic analysis of Fourier series. The chapter presents the solution of a problem of the convergence of the Fourier series for a given function; this solution can be obtained by the application of Dirichlet's theorem. It also presents a few examples to simplify the evaluation of the Fourier coefficients by making use of the evenness or oddness of the expanded f(x). The total interval (-π,π can be divided into a finite number of parts such that f(x) varies monotonically in each. A function satisfies Dirichlet conditions in the interval (-π,π) if it is either continuous in the interval or has a finite number of discontinuities of the first bind, and if, furthermore, the interval can be divided into a finite number of subintervals in each of which f(x) varies monotonically.
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