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## Main Question or Discussion Point

let be [tex] f(x) \sim g(x) [/tex] , in the sense that for big x f(x) is asymptotic to g(x) , my question if what happens to their Laplace transform ??

i belive that [tex] \int _{0}^{\infty}dt f(t)exp(-st) \approx \int _{0}^{\infty}dt g(t)exp(-st) [/tex]

in first approximation the Laplace transform of f(x) and the Laplace transform of g(x) must be equal.

another question if we had a Linear operator L so we can define its inverse L^{-1} is it true that [tex] f(x) \sim L(g(x)) \rightarrow L^{-1} f(x)= g(x) [/tex]

i belive that [tex] \int _{0}^{\infty}dt f(t)exp(-st) \approx \int _{0}^{\infty}dt g(t)exp(-st) [/tex]

in first approximation the Laplace transform of f(x) and the Laplace transform of g(x) must be equal.

another question if we had a Linear operator L so we can define its inverse L^{-1} is it true that [tex] f(x) \sim L(g(x)) \rightarrow L^{-1} f(x)= g(x) [/tex]