Exponentially shifted semigroup
= Exponentially shifted semigroup
If $U(t)$ has generator $A$, then $\widehat U(t)=e^{-\omega t}U(t)$ has generator $A-\omega I$. This shift converts a growth bound $Me^{\omega t}$ into the uniform bound $M$.
= Exponentially shifted semigroup
If $U(t)$ has generator $A$, then $\widehat U(t)=e^{-\omega t}U(t)$ has generator $A-\omega I$. This shift converts a growth bound $Me^{\omega t}$ into the uniform bound $M$.