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 , . 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)?

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 GrunwaldLetnikov differintegral for evaluating , but so far this has been futile).

Well, I managed to finally prove it.