- #1

mclaudt

- 6

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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?