The asymptotic theorem of I. Babushka (Q1385882)

The author starts from the remark that for reflexive Banach spaces of integrable functions the error functional of a cubature formula is optimal if and only if its extremal function vanishes at the nodes of the cubature formula. He establishes an asymptotic variant of this result for Banach spaces of periodic functions which asserts that a sequence of error functionals is asymptotically optimal if and only if it has a sequence of asymptotically extremal functions that vanish at the nodes.