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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).

MSC:

41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A25 Rate of convergence, degree of approximation
41A50 Best approximation, Chebyshev systems

Citations:

Zbl 0162.361
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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).
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