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Properties of Heaviside’s Unit Step Function Based on Laplace – Stieltjes Transform

N. M. Sharma and P. A. Gulhane

Laplace-Stieltjes transform is one of the flourishing field of active research due to its wide range of applications. Purpose of this paper is to prove some properties of unit step function with the help of Laplace - Stieltjes transform. It seldom matters what value is used for U (0), since U is mostly used as a distribution. Some common choices are the function is used in the mathematics of control theory and signal processing to represent a signal that switches on at a specified time and stays switched on indefinitely. It is also used in structural mechanics together with the Dirac Delta function to describe different types of structural loads.