Laplace transform sqaured differential

[opul]

Hi

I was wondering what the Laplace transform of a squared differential is.
With that I mean the Laplace of (y' )^2 (this being y'*y' and not the second order derivative). So for example velocity squared.

 

[rbj]

there is a lot of similarity between the Fourier Transform and the Laplace Transform. the F.T. is really just the L.T. with the real part of $s = \sigma + i \omega$ set to zero. try to answer the question regarding the F.T. and see if you can generalize.

 

[the_wolfman]

I don't know the exact form off the top of my head, but it will be an ugly convolution of the form:

integral (s^2 F(a)F(a-s) da)