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Also, the kernel of the laplace transform is ##\exp(-st)##, very similar to kernel of the fourier, that is ##\exp(-i \omega t)##, and and same question again, if ωt is equal to θ thus st is equal to what??

Finally, I see sometimes a connection between s and ω, that is ##s = \sigma + i \omega##, but, again, what this equation means and what is σ?