The scientist and engineers guide to digital signal processing, Steven W. Smith, p. 134-135 states:
[...] imagine a linear system receiving an input signal, $x[n]$. and generating an output signal, $y[n]$. Now suppose the input signal is changed in some linear way, resulting in a new input signal, which we will call $x'[n]$. This results in a new output signal, $y'[n]$. The question is, how does the change in the input signal relate to the change in the output signal? The answer is: the output signal is changed in exactly the same linear way that the input signal was changed. [...] A linear change made to the input signal results in the same linear change to the output signal.'
I assume this can be written for the continuous case as:
If $g = L(f)$, then $M(g) = L(M(f))$
where $L, M$ are linear (LTI) operators, $f, g$ are functions corresponding to $x[n], y[n]$ and $M(f), M(g)$ correspond to $x'[n], y'[n]$.
My question is: is this true for the continuous case?
Any references, or a proof would be appreciated.
This question is a near duplicate of this question (answered) and also this one (now deleted). I am sorry about this-spent much time on the web but only found the reference I quoted-but really need an answer asap.