Yes, I tried that, and it just doesn't fit..
P(\tau)S(\tau)u(t)=P(\tau)u(t-\tau)=u(t-\tau) if t-\tau<=\tau and 0 for t-\tau>\tau
S(\tau)P(0)u(t)=S(\tau)u(t) for t<=0 and 0 otherwise=u(t-\tau) if t<=0 and 0 otherwise..
Well, something's got to be wrong here, but I can't see what..
Assume u:R\rightarrow C^n and define shift operator S(\tau) with
S(\tau)u(t)=u(t-\tau)
and truncation operator P(\tau) with
P(\tau)u(t)=u(t) for t\leq\tau and 0 for t>\tau
Then P(\tau)S(\tau)=S(\tau)P(0) for every \tau>=0.
Can someone please prove last statement..