The Application Of Tauber Theorem In The Fourier Series

In mathematics, the theory of Fourier series is mainly about the question of whether the Fourier series of a periodic function converges to the given function. Convergence is not necessarily given in the general case, and certain criteria must be met for convergence to occur. The subject of divergent series, as a domain of mathematical analysis, is primarily concerned with a broad sense sum of divergence series such as Abel sum, Cesaro sum and Borel sum.In this paper, we present Tauberian theorems for this question, which give conditions for a series summable by some method to be summable in the broad sense. As a conse-quence, we prove that the convergence and uniform convergence of the Fourier series under a suitable Tauberian condition.