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Question Number 77536 by ~blr237~ last updated on 07/Jan/20

$$\mathrm{find}\mathrm{all}\mathrm{function}\mathrm{that}\mathrm{satisfy}$$$$\mathrm{\forall }\mathrm{p}>0{\int }_0^{\mathrm{\infty }}\mathrm{f}\left(\mathrm{t}\right){\mathrm{e}}^{-\mathrm{pt}}\mathrm{dt}={\mathrm{e}}^{-\mathrm{pT}}\mathrm{with}\mathrm{T}\mathrm{a}\mathrm{positive}\mathrm{real}$$

Answered by JDamian last updated on 07/Jan/20

$$Accordingtothe\mathit{L}\mathit{a}\mathit{p}\mathit{l}\mathit{a}\mathit{c}\mathit{e}\mathit{T}\mathit{r}\mathit{a}\mathit{n}\mathit{s}\mathit{f}\mathit{o}\mathit{r}\mathit{m}$$$$tables$$$$$$$$f\left(t\right)=\delta (t-T)$$$$$$$$whichisknownas\mathit{d}\mathit{e}\mathit{l}\mathit{a}\mathit{y}\mathit{e}\mathit{d}\mathit{i}\mathit{m}\mathit{p}\mathit{u}\mathit{l}\mathit{s}\mathit{e}.$$

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