Shift invariant operators and a saturation theorem
The properties of shift invariant operators $Q_h$ are proved: It is shown that $Q$ has polynomial order $r$ iff $r$ is the rate of convergence of $Q_h$. A weak saturation theorem is given. If $f$ is replaced by $Q_hf$ in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.