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http://hdl.handle.net/11701/17324
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Поле DC | Значение | Язык |
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dc.contributor.author | Vinogradov, Oleg L. | - |
dc.date.accessioned | 2020-04-10T12:17:09Z | - |
dc.date.available | 2020-04-10T12:17:09Z | - |
dc.date.issued | 2020-03 | - |
dc.identifier.citation | Vinogradov 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.identifier.other | https://doi.org/10.21638/11701/spbu01.2020.102 | - |
dc.identifier.uri | http://hdl.handle.net/11701/17324 | - |
dc.description.abstract | An 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.sponsorship | This work is supported by the Russian Science Foundation under grant No. 18-11-00055. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1 | - |
dc.subject | Jackson inequality | en_GB |
dc.subject | splines | en_GB |
dc.subject | sharp constants | en_GB |
dc.title | Sharp Jackson - Chernykh type inequality for spline approximations on the line | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 1 |
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Файл | Описание | Размер | Формат | |
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15-27.pdf | 342,54 kB | Adobe PDF | Просмотреть/Открыть |
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