On Jackson's theorems in \(L_ 2\) (Q1813365)

Estimates for \(E_ n(f)\) by means of iterated differences of derivates are investigated and characterizations of finite sets are given on which the differences are considered. In particular, if \(\Delta^ mf^{(r)}, r>0\), is taken into account and \(1/q\leq r/m<1/(q-1)\), \(q\) an integer, then it is shown that the cardinality of the sets in question is estimated by \(q+1\) from below and there is no analogue for \(r=0\).