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 2010-01-16, 00:06 #1 flouran     Dec 2008 34116 Posts Inverse Laplace Transform I was looking through some tables of Laplace Transforms on f(t) the other day, and I noticed that in all cases, as $s \to \infty$, $F(s) \to 0$. A question that I have been trying to prove is that if $\lim_{s\to\infty}F(s) = 0$, then does that necessitate whether $F(s)$ can undergo an inverse Laplace transform (i.e. by the Bromwich integral)? I suspect that the answer is "no", but if anyone has some attempt at a proof I would appreciate it (my idea would be to use Post's inversion formula and utilizing the Grunwald-Letnikov differintegral for evaluating $F^{(k)}\left(\frac{k}{t}\right)$, but so far this has been futile).
2010-01-18, 23:48   #2
flouran

Dec 2008

72×17 Posts

Quote:
 Originally Posted by flouran I was looking through some tables of Laplace Transforms on f(t) the other day, and I noticed that in all cases, as $s \to \infty$, $F(s) \to 0$. A question that I have been trying to prove is that if $\lim_{s\to\infty}F(s) = 0$, then does that necessitate whether $F(s)$ can undergo an inverse Laplace transform (i.e. by the Bromwich integral)?
No.
Quote:
 Originally Posted by flouran I suspect that the answer is "no", but if anyone has some attempt at a proof I would appreciate it (my idea would be to use Post's inversion formula and utilizing the Grunwald-Letnikov differintegral for evaluating $F^{(k)}\left(\frac{k}{t}\right)$, but so far this has been futile).
Well, I managed to finally prove it.

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