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Let $f(t)$ be a function (for example of time $t$).

Is there a general expression of the laplace transform of $\sqrt{f(t)}$ ?

Same question for the inverse Laplace transform : Let $f(s)$ be the Laplace transform of $f(t)$, is there a generic expression of the inverse Laplace transform of $\sqrt{f(s)}$ ?

edit: One special case is known: the Laplace transform of $f(t)=t$. It is often tabulated, like in this table from Lamar University, Texas.

edit2: I have no idea how to prove such a general transform exists. Perhaps it does not and in this case I would be very grateful for a link or an explaination.

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You can start by trying special cases like $\sqrt{t}$, $\sqrt{e^t}$. But, for example,$\sqrt{\sin t}$ would be undefined. –  Pedro Tamaroff Feb 5 '12 at 19:24
Why should there be? –  Fabian Feb 5 '12 at 19:38

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