we know that if we have a function f(x), and we call g(w) its fourier transform, then the fourier transform of x f(x) is
and viceversa dx(f(x)) becomes
i w g(w)
So i needed to transform an operator, for example
L(u):= u+x^2 u+dx(u)
I need the transform of L, that is:
U-(second derivative(U))+i w u
How can i automatically transform the variable x in a derivative, and x^n in a derivative of order n, and viceversa?