What's the connection between the Laplace transform and the Fourier transform?

fourier-analysis functional-analysis spectral-theory integral-transforms

Solution 1:

I don't know what answer you are looking for but for example both Laplace and Fourier transform are a so called Gelfand Transform.

You can find good introduction to Gelfand Transform in nice book Functional analysis for probability and stochastic processes: an introduction, A. Bobrowski. Look into Chapter 6.

Solution 2:

Laplace transform and Fourier transform are both special cases of the http://en.wikipedia.org/wiki/Linear_canonical_transformation.

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