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41-XX Approximations and expansions
41Axx Approximations and expansions
41A80 Remainders in approximation formulas

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Shift invariant operators and a saturation theorem

Karol Dziedziul (2003)

Applicationes Mathematicae

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 $Q_{f} h$ in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.

Some inequalities connected with an approximate integration.

Wa̧sowicz, Szymon (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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