Is there a function equal to its Laplace transform?
I mean
$ \int_{0}^{\infty}dt\exp(-st)f(t)= f(s).$
Of course I know $f(t)=0 $ satisfy the equation.
For the case of the Fourier transform, I know the Hermite Polynomials are eigenfunction of the Fourier transform, perhaps it's enough with a shift or rotation into the complex plane ($s \rightarrow i\omega$)?