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dc.contributor.authorVinogradov, Oleg L.-
dc.identifier.citationVinogradov O. L. Sharp Jackson - Chernykh type inequality for spline approximations on the line. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 15–27.en_GB
dc.description.abstractAn analog of the Jackson Chernykh inequality for spline approximations in the space L2(R) is established. For r 2 N, σ > 0, we denote by A r(f)2 the best approximation of a function f 2 L2(R) by the space of splines of degree r and of minimal defect with knots j , j 2 Z, and by ω(f, δ) its first order modulus of continuity in L2(R). The main result of the paper is the following. For every f 2 L2(R) A r(f)2 6 1 p2 ω f, θrπ σ 2 , where εr is the positive root of the equation 4ε2(ch " − 1) ch " + cos = 1 32r−2 , τ = p1 − ε2, θr = 1 p1−"2 r . The constant 1 p2 cannot be reduced on the whole class L2(R), even if one insreases the step of the modulus of continuity.en_GB
dc.description.sponsorshipThis work is supported by the Russian Science Foundation under grant No. 18-11-00055.en_GB
dc.publisherSt Petersburg State Universityen_GB
dc.relation.ispartofseriesVestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1-
dc.subjectJackson inequalityen_GB
dc.subjectsharp constantsen_GB
dc.titleSharp Jackson - Chernykh type inequality for spline approximations on the lineen_GB
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