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?