<Dd> f ^ (ξ 2) = δ (ξ 1 − ξ 2) (\ displaystyle (\ hat (f)) (\ xi _ (2)) = \ delta (\ xi _ (1) - \ xi _ (2))) </Dd> <P> which again follows by imposing self - adjointness of the Fourier transform . </P> <P> By analytic continuation of the Fourier transform, the Laplace transform of the delta function is found to be </P> <Dl> <Dd> ∫ 0 ∞ δ (t − a) e − s t d t = e − s a . (\ displaystyle \ int _ (0) ^ (\ infty) \ delta (t-a) e ^ (- st) \, dt = e ^ (- sa).) </Dd> </Dl>

Difference between delta function and dirac delta function