Laplace transform and fourier transform

[coordinates]

Homework Statement

F{f(t)} is the Fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t)

why F{f(t)} = L{f(t)} where s = jw in L{f(t)}

The Attempt at a Solution

I suppose the definition of F{f(t)} is

∫[f(t)e^-jwt]dt

where the lower integral limit is -∞ and higher intergral limit is +∞.

And I suppose the definition of L{f(t)} is

∫[f(t)e^-st]dt

where the lower integral limit is -∞ and higher integral limit is +∞.(that is bilateral Laplace transform)

and i think it is obviously to say F{f(t)} = L{f(t)} where s = jw in L{f(t)} just by substitute s = jw in ∫[f(t)e^-st]dt.

My solution is so simple that I can't believe it's a problem assigned by my professor!
Some guy please tell me if I am correct or not, and where it is.

Any reference or advise will be appreciated.

thanks in advance.

 

[susskind_leon]

Yes you are correct, as long as the imaginary axis is inside the region of convergence.

 

[coordinates]

Yes you are correct, as long as the imaginary axis is inside the region of convergence.

3x~ I am more confident~