Some applied aspects of the Dirac delta function

Abstract

The study is devoted to some applied aspects of the Dirac delta function. On the basis of this function, an integral representation was found for the deviation of the functions of the Holder class ${H}^{\alpha }$ ($0<\alpha <1$) from their Poisson integrals in the upper half-plane. In the current research, exact equalities of the upper bounds for the deviations of the functions of the Holder class ${H}^{\alpha }$ from the Poisson operators in the upper half-plane were found by applying the known properties of the Dirac delta function.