Transfer Function vs Frequency Response Talking about Butterworth filters my prof said that a filter is described by its frequency response $H(\omega )$.

What I think is that filter is really described by its transfer function, since there can exist many transfer functions that share the same $H(\omega )$.
Was my prof wrong?
Was my prof wrong? 


No. You're right, you can find multiple systems with the same frequency response, or the same transfer function.

But if you're using something as a (linear, which is often implied) filter, then all you care about is the frequency response (otherwise, you'd probably not be calling the thing "filter"). So, when I define a filter, it's usually sufficient to specify $H(\omega)$.