- #1
tutumar
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Assume u:R[itex]\rightarrow[/itex] C^n and define shift operator S([itex]\tau[/itex]) with
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..
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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