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Patterns_ to define linear operators?


Hello,
I'd like to implement a rule that will factor out constants from 
linear operators such as FourierTransform; i.e.,
FourierTransform[a*f[x], x, k]  to a*FourierTransform[f[x],x,k]

Here is a method that seems sensible at first, but is potentially 
dangerous:

MyRule1 =
FourierTransform[a_ f_[y_], x_, k_] :-> a FourierTransform[f[y],x,k]
(which would fail if a was not free of x)

An improvement is:

MyRule2 =
FourierTransform[a_?(FreeQ[#,x]&), f_[y_], x_, k_] :-> a FourierTransform[f[y],x,k]
(which would fail if a were a product, say b x)

Does anybody have advice on a robust way to implement this rule?

Thanks, Craig Carter


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