Re: Questions on Laplace transform

The World Wide Wade wrote:
In article <EsOXj.147767$Cj7.118577@pd7urf2no>,
Rskater <Rskater@xxxxxxxxxxx> wrote:


The World Wide Wade wrote:


Okay for what? Rephrase your question precisely.

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)>0 for s>=0 then f(x) >0 for x>0.


No, I already gave a counterexample: 2e^(-2x) - e^(-x).
LT of your example is s/(s+1)/(s+2) which is 0 when s=0.
Am I missing something.
.

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