Re: Questions on Laplace transform

The World Wide Wade wrote:
In article <xyCXj.146482$Cj7.112637@pd7urf2no>,
Rskater <Rskater@xxxxxxxxxxx> wrote:


The World Wide Wade wrote:

In article <lppXj.144599$Cj7.137009@pd7urf2no>,
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).

Thank you for the counter example.

So, if I have F(s)> 0 for 0<s<1, would that work.


No, look at 2e^(-2x) - e^(-x). In this case F(s) > 0 for s > 0.
Thanks.

So F(s) >0 for s>=0 would be okay?

.

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