Suppose I know the laplace transform of $f(t)$. What would be the relation between laplace transform of $f(t)$ and laplace transform of $(f(t))^2$? Thanks in advance.
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2The "Multiplication" entry in this table of Laplace transform properties on Wikipedia gives a result for the Laplace transform of $f(t)g(t)$ as a convolution integral of the transforms of $f(t)$, $g(t)$. – Semiclassical Dec 28 '16 at 05:30
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1I'm affraid you need the Fourier/Laplace inversion theorem for showing that it is $\frac{1}{2i\pi} \int_{\sigma -i\infty}^{\sigma+i \infty} F(u)F(s-u)du$ – reuns Dec 28 '16 at 05:38
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3Possible duplicate of [Laplace transform of $[f''[x]]^n$](http://math.stackexchange.com/questions/32829/laplace-transform-of-fxn) – polfosol Dec 28 '16 at 08:41