Inverse Fourier Transform of (e^w)*F(w)

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If the inverse Fourier Transform of F(w) is f(t), what is the inverse Fourier Transform of (e^w)*F(w) ? My best guess is that I should expand e^w into a power series and use the fact that the inverse transform of ((iw)^n)*F(w) is the nth derivative of f(t). Is there a better way?

Bob