Questions on Laplace transform

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
.

Relevant Pages

  • Re: generalized Thevenin?
    ... If its a resistor and a capacitor then what? ... For passive components is Z a linear differential equation? ... Laplace transform of the impedance. ...
    (sci.electronics.design)
  • Re: inverse laplace transform
    ... I'm working on trying to model a non-linear system (described by a ... The Laplace transform only work with linear ... Lyons' book and I see that he calls it a linear system. ... Wescott Design Services ...
    (comp.dsp)
  • Re: inverse laplace transform
    ... The Laplace transform only work with linear ... Lyons' book and I see that he calls it a linear system. ... follow the impulse invariance IIR filter design method. ... Impulse-invariance makes sense in the high-falutin' world of mathematics, but it only translates if you treat the discrete-time stuff as a true chain of impulses that get run through a reconstruction filter, etc. ...
    (comp.dsp)
  • Re: Why relativity does not applies in Industry???
    ... approximation only. ... smelly foot in your smelly mouth. ... Or in fact EITHER a linear or an exponential function. ...
    (sci.physics.relativity)
  • Re: Why relativity does not applies in Industry???
    ... You equate 'proportional' to 'linear'. ... Proportional implies ... but it is not necessarily a FIXED ratio. ...
    (sci.physics.relativity)