Laplace Transform of Null Function

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Theorem

Let $\mathcal N: \R \to \R$ be a null function.


The Laplace transform of $\map {\mathcal N} t$ is given by:

$\laptrans {\map {\mathcal N} t} = 0$


Proof

\(\displaystyle \laptrans {\map {\mathcal N} t}\) \(=\) \(\displaystyle \int_0^{\to +\infty} e^{-s t} \map {\mathcal N} t \rd t\) Definition of Laplace Transform



Sources