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Old 2010-01-16, 00:06   #1
flouran
 
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Post 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).
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Old 2010-01-18, 23:48   #2
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Quote:
Originally Posted by flouran View Post
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 View Post
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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