Local properties of fourier series via deferred Riesz mean

Abstract

The convergence of Fourier series of a function at a point depends upon the behaviour of the function in the neighborhood of that point, and it leads to the local property of Fourier series. In the proposed work, we introduce and study the absolute convergence of the deferred Riesz summability mean, and accordingly establish a new theorem on the local property of a factored Fourier series. We also suggest a direction for future researches on this subject, which are based upon the local properties of the Fourier series via basic notions of statistical absolute convergence.