TITLE:
Application of Exponential Kernel to Laplace Transform
AUTHORS:
Sami M. AL-Jaber
KEYWORDS:
Kernels, Integral Transforms, Laplace Transforms, Singularity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.5,
May
27,
2019
ABSTRACT: In this paper, the exponential
decreasing kernel is used in Laplace integral transform to transform a function
from a certain domain to another domain. It is shown, in a rigorous way, that the
Laplace transform of the delta function is exactly one half rather than one, as
it is believed. In addition, when this kernel is used in integral transform of
attractive and repulsive Coulomb potential, it yields a finite definite value
at the point of singularity.