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Student Support Forum: 'fourier transform of an operator' topicStudent Support Forum > General > "fourier transform of an operator"

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andrea
12/13/12 12:54pm

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
i dw(g(w))
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?
thanks!

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