MMfE - Is Laplace Transformable

• Online Resource: Laplace Transformable, Abbiscia of Absolute Convergence

If:

$$\exists \alpha \in \mathbb{R},M>0:|u(t)|\le M{e}^{\alpha t}\text{for}t>0$$

Then: $u(t)$ is of exponential order and is Laplace Transformable.

According to the [ Riemann-Fourier Theorem ] the antri-transform of the function $U(s)=\mathcal{L}[u(t)]$, so $u(t)$ is equal to:

$$u(t)=\frac{1}{2\pi }\underset{R\to +\infty }{\lim }{\int }_{-R}^{+R}{e}^{(x+iy)t}\cdot U(x+iy)dt$$

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• Online Resource: PDF

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