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# Inverse laplace transform of step function

Posted 10 years ago
 I tried to do InverseLaplaceTransform[HeavisideTheta[s],s,t]  and didn't get anything. any suggestions?
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Posted 10 years ago
 Observe In[15]:= InverseLaplaceTransform[LaplaceTransform[HeavisideTheta[s], s, t], t, s] Out[15]= 1 despite the statement in the reference: LaplaceTransform and InverseLaplaceTransform are mutual inverse In[16]:= InverseLaplaceTransform[LaplaceTransform[y[s], s, t], t, s] Out[16]= y[s] Does this entitle anybody to consider In[4]:= InverseLaplaceTransform[1, s, t] Out[4]= DiracDelta[t] DiracDelta as InverseLaplaceTransform of HeavisideTheta? Rather not, DiracDelta is the InverseLaplaceTransform of 1, but not of HeavisideTheta. If Mathematica tells the truth, an InverseLaplaceTransform of HeavisideTheta does not exist, at least I did not find one in the books. What do you thing the result of In[1]:= InverseLaplaceTransform[HeavisideTheta[s], s, t] Out[1]= InverseLaplaceTransform[HeavisideTheta[s], s, t] should be?
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