Statistical convergence of sequences and series of complex numbers with applications in Fourier Analysis and Summability

This is a survey paper on recent results indicated in the title. In contrast to the famous examples of Kolmogorov and Fejér on the pointwise divergence of Fourier series, the statistical convergence of the Fourier series of any integrable function takes place at almost every point; and the statistical convergencr of the Fourier series of any continuous function is uniform. Furthermore, Tauberian conditions are also presented, under which ordinary convergence of any sequence of real or complex numbers follows from its statistical summability.