Re: Questions on Laplace transform
- From: Rskater <Rskater@xxxxxxxxxxx>
- Date: Sat, 17 May 2008 15:09:17 GMT
The World Wide Wade wrote:
In article <lppXj.144599$Cj7.137009@pd7urf2no>,Thank you for the counter example.
Rskater <Rskater@xxxxxxxxxxx> wrote:
Let us assume f(x) is a linear combination of an exponential function.
i.e. \[ f(x) = \sum_{i=1}^n a_i \exp(-b_i x) \] with $b_i>0$ for all i,
but some of $a_i$'s could be negative.
Also assume F(s) is the Laplace Transform of f(x).
Is the following true?
If F(s) has no positive roots then f(x) >0 for x>0.
Thanks
No, try f(x) = e^(-x) - 2e^(-2x).
So, if I have F(s)> 0 for 0<s<1, would that work.
.
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