Transfer function is something every engineer studies during his early career. I thought people like Fourier and Green had developed it, but apparently it stems from Kubo's linear response formula. Is it true?
This formalism also arises in the LTI (linear time invariant) theory.
For example from the wiki linear response page:
Consider a damped harmonic oscillator with input given by an external driving force $h(t)$,
$$\ddot{x}(t)+\gamma \dot{x}(t)+\omega_0^2 x(t)=h(t). $$
The complex-valued Fourier transform of the linear response function is given by:
$$\tilde{\chi}(\omega) = \frac{\tilde{x}(\omega)}{\tilde{h}(\omega)} = \frac{1}{\omega_0^2-\omega^2+i\gamma\omega}$$