Question Number 77536 by ~blr237~ last updated on 07/Jan/20
$$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$ $$\:\:\forall\:\mathrm{p}>\mathrm{0}\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{pt}} \mathrm{dt}=\:\mathrm{e}^{−\mathrm{pT}} \:\:\:\:\:\:\mathrm{with}\:\mathrm{T}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real} \\ $$
Answered by JDamian last updated on 07/Jan/20
$${According}\:{to}\:{the}\:\boldsymbol{{Laplace}}\:\boldsymbol{{Transform}} \\ $$ $${tables} \\ $$ $$ \\ $$ $${f}\left({t}\right)=\delta\left({t}−{T}\right) \\ $$ $$ \\ $$ $${which}\:{is}\:{known}\:{as}\:\boldsymbol{{delayed}}\:\boldsymbol{{impulse}}. \\ $$