Sorry for thumb terminology, I just would like to grasp the main idea, as a physicist, without unnecessary complications, associated with system of axioms and definitions.(adsbygoogle = window.adsbygoogle || []).push({});

Fourier transform can be seen as rotation of basis in space of all complex-valued functions from basis of delta-functions to a new basis of waves [itex]e^{i\omega t}[/itex].

Laplace transform can be seen as generalization of Fourier transform to complex frequencies. Is it correct to see the Laplace transform as a rotation of basis in space of complex-valued functions of complex argument, from delta-functions basis to a new basis of [itex]e^{(\alpha + i\beta) t}[/itex]and, if it is so, what is the basis in that space, and why does summation go only along line [itex](-\infty, +\infty)[/itex] in direct transform and [itex](\gamma - i\infty, \gamma + i\infty)[/itex] in reverse transform?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Laplace transform as rotation. In what space?

**Physics Forums | Science Articles, Homework Help, Discussion**