View Single Post
Old 2010-01-16, 00:06   #1
flouran's Avatar
Dec 2008

72·17 Posts
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).
flouran is offline   Reply With Quote