A Green's function is defined as the solution of an equation which sets a linear operator equal to a value of this function, and one method of deriving it is taking the derivative of the Heaviside Step Function.
Mikusinski's identity gives the square root of this function, and the integral of this function of x minus y times f of x is equal to f of y, meaning it obeys the sifting property, which makes it the convolution function's identity operator. A Green's function is defined as the solution of an equation which sets a linear operator equal to a value of this function, and one method of deriving it is taking the derivative of the Heaviside Step Function. A group of them is known as their namesake's "comb". Usually shown as an up-arrow, it represents the limit of a statistical distribution as the standard deviation goes to zero. For 10 points, name this function useful for defining impulsive forces, which is infinite in a single point and zero elsewhere.
Mikusinski's identity gives the square root of this function, and the integral of this function of x minus y times f of x is equal to f of y, meaning it obeys the sifting property, which makes it the convolution function's identity operator.
{Dirac Delta} Function