Assume u:R[itex]\rightarrow[/itex] C^n and define shift operator S([itex]\tau[/itex]) with(adsbygoogle = window.adsbygoogle || []).push({});

S([itex]\tau[/itex])u(t)=u(t-[itex]\tau[/itex])

and truncation operator P([itex]\tau[/itex]) with

P([itex]\tau[/itex])u(t)=u(t) for t[itex]\leq[/itex][itex]\tau[/itex] and 0 for t>[itex]\tau[/itex]

Then P([itex]\tau[/itex])S([itex]\tau[/itex])=S([itex]\tau[/itex])P(0) for every [itex]\tau[/itex]>=0.

Can someone please prove last statement..

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# Causality with time invariance

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