I've been wondering whether the Laplace transform is injective. Suppose I have that(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int^{∞}_{0}e^{-st}f(t)dt = \int^{∞}_{0}e^{-st}g(t)dt [/tex] for all s for which both integrals converge. Then is it true that [itex] f(t) = g(t) [/itex] ? If so, any hints on how I might prove it?

Thanks!

BiP

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# Is the inverse of the Laplace transform unique?

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