It has been proved that the inverse operator is the solution of the related equation of the following form, in which the non-homogeneous term has been substituted by the Dirac's delta function :
It should be noted that the Dirac's delta function, because of its rather complex nature, is formally described in terms of the derivative of the Heaviside unit step function :
Diagrams of the Dirac's delta function and Heaviside unit step function are schematically shown in Fig.
Following the method described in [17,20], it is required to solve the following differential equation, by making use of the Dirac's delta function:
It requires the Dirac's delta function to be expanded in the same way, i.
m], however, can be found easily recalling the sifting property of the Dirac's delta function: