Yudin, V. A. Multidimensional Jackson theorem in \(L_ 2\). (English. Russian original) Zbl 0475.41013 Math. Notes 29, 158-162 (1981); translation from Mat. Zametki 29, 309-315 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 Documents MSC: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) 41A25 Rate of convergence, degree of approximation 41A50 Best approximation, Chebyshev systems Keywords:Jackson inequality; upper bounds Citations:Zbl 0162.361 PDFBibTeX XMLCite \textit{V. A. Yudin}, Math. Notes 29, 158--162 (1981; Zbl 0475.41013); translation from Mat. Zametki 29, 309--315 (1981) Full Text: DOI References: [1] N. I. Chernykh, ?On the Jackson inequality in L2,? Tr. Mat. Inst. Akad. Nauk SSSR,88, 71-74 (1967). [2] N. I. Chernykh, ?On the best approximation of periodic functions by trigonometric polynomials in L2,? Mat. Zametki,2, No. 5, 513-522 (1967). [3] R. Courant and D. Hubert, Methods of Mathematical Physics [Russian translation], Vol. 1, Gostekhizdat, Leningrad (1951). [4] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge (1922). · JFM 48.0412.02 [5] V. A. Yudin, ?The multidimensional Jackson theorem,? Mat. Zametki,20, No. 3, 439-444 (1976). [6] V. Yu. Popov, ?On the best mean-square approximations of functions of m variables,? Mat. Zametki,14, No. 6, 913-924 (1973). 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.