20100116, 00:06  #1 
Dec 2008
7^{2}×17 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 , . A question that I have been trying to prove is that if , then does that necessitate whether 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 GrunwaldLetnikov differintegral for evaluating , but so far this has been futile). 
20100118, 23:48  #2  
Dec 2008
7^{2}·17 Posts 
Quote:
Well, I managed to finally prove it. 

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