On a Local Equality of Distributions and Relation of Jumps of Distributions with Fourier Series

Abstract

Distribution theory has an important role in applied mathematics. Firstly, in the introduction part of this paper we will give some general notations, definitions and results in distribution theory, as analytic representation of distribution, distributional jump behavior, distributional symmetric jump behavior, tempered distributions, formulas for the jump of distributions in terms of Fourier series and global equality in distributional sense. Then in final part we will state two results, the first one has to do on local equality of two distributions and the second one states if a 2π− periodic distribution has jump behavior at point, then exists the relation of jumps of distributions with Fourier series in a subset of the upper half-plane.