Yudin, A. A.; Yudin, V. A. On Jackson’s theorems in \(L_ 2\). (English. Russian original) Zbl 0737.42001 Math. Notes 48, No. 4, 1071-1074 (1990); translation from Mat. Zametki 48, No. 4, 152-157 (1990). 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 \(r=0\). Reviewer: M.Krbec (Praha) Cited in 2 Documents MSC: 42A10 Trigonometric approximation 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) Keywords:modulus of continuity; best approximation; Jackson’s theorem; iterated differences of derivates PDFBibTeX XMLCite \textit{A. A. Yudin} and \textit{V. A. Yudin}, Math. Notes 48, No. 4, 1071--1074 (1990; Zbl 0737.42001); translation from Mat. Zametki 48, No. 4, 152--157 (1990) Full Text: DOI References: [1] N. I. Chernykh, ?On Jackson’s inequality in L2,? Transactions of Math. Institute of Academy of Science of the USSR,88, 71-74 (1967). [2] N. I. Chernykh, ?On the best approximation of periodic functions by trigonometric polynomials in L2,? Matem. Zametki,2, No. 5, 513-522 (1967). [3] V. A. Yudin, ?On Jackson’s theorems in L2,? Matem. Zametki,41, No. 1, 43-47 (1987). [4] J. W. S. Cassels, Introduction to Diophantine Approximations, Cambridge University Press (1957). · Zbl 0077.04801 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.