Topics: Laplace Transform

Concerning Laplace transforms, we can guarantee their existence by means of the consequences of the following theorems.

(theorem, 8)

Note that, as increases, the growth of the module of the function is not greater than that of an exponential function. That is, there exists and such that, for every value of :

We call the growth exponent of the function . This condition guarantees the existence of the Laplace transform.


If is piecewise continuous in every finite set of exponential order for , then the Laplace transform exists as long as .