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How to prove that the inverse Laplace Transform of zero is zero itself?

$$\mathscr{L}^{-1}\{0\}=0$$

I know that the inverse Laplace Transform of a constant is Dirac's Delta. But I think that that applies only to positive constants.

Thanks

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1 Answer

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If $\mathcal{L}(f) = F$, then $\mathcal{L}^{-1}(F) =f$. $\mathcal{L}(0) = 0$ because $\mathcal{L}$ is a linear operator. Or you can actually compute $\mathcal{L}(0)$ using the definition.

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