Geodesic
Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 32-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents a new technique for deriving the estimates mentioned in the title. In particular, this technique allows one to establish Jackson-type inequalities for moduli of continuity of arbitrary order with relatively small constants. The results obtained are valid in different spaces of periodic and nonperiodic functions. 
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     title = {Estimates for functionals with a~known finite set of moments in terms of deviations of operators constructed with the use of the {Steklov} averages and finite differences},
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O. L. Vinogradov; V. V. Zhuk. Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 32-66. http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a1/

[1] N. P. Korneichuk, Tochnye konstanty v teorii priblizheniya, M., 1987 | MR

[2] O. L. Vinogradov, V. V. Zhuk, “Otsenki funktsionalov s izvestnoi posledovatelnostyu momentov cherez otkloneniya srednikh tipa Steklova”, Zap. nauchn. semin. POMI, 383, 2010, 5–32 | MR

[3] O. L. Vinogradov, V. V. Zhuk, “Skorost ubyvaniya konstant v neravenstvakh tipa Dzheksona v zavisimosti ot poryadka modulya nepreryvnosti”, Zap. nauchn. semin. POMI, 383, 2010, 33–52 | MR

[4] N. I. Akhiezer, Lektsii po teorii approksimatsii, M., 1965

[5] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, M., 1974

[6] B. M. Levitan, Pochti-periodicheskie funktsii, M., 1953

[7] O. L. Vinogradov, “Tochnye neravenstva tipa Dzheksona dlya priblizhenii klassov svertok tselymi funktsiyami konechnoi stepeni”, Algebra i analiz, 17:4 (2005), 59–114 | MR | Zbl

[8] R. Grekhem, D. Knut, O. Patashnik, Konkretnaya matematika, M., 1998

[9] O. L. Vinogradov, V. V. Zhuk, “Otsenki funktsionalov s izvestnym konechnym naborom momentov cherez moduli nepreryvnosti vysokikh poryadkov”, Metody splain-funktsii, Rosc. konf., posv. 80-letiyu so dnya rozhd. Yu. S. Zavyalova (Novosibirsk, 31 yanvarya – 2 fevralya 2011 g.), Tez. dokl., Novosibirsk, 2011, 29–30

[10] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, M., 1977 | MR

[11] O. L. Vinogradov, V. V. Zhuk, “Tochnye neravenstva tipa Kolmogorova dlya modulei nepreryvnosti i nailuchshikh priblizhenii trigonometricheskimi mnogochlenami i splainami”, Zap. nauchn. semin. POMI, 290, 2002, 5–26 | MR | Zbl

[12] O. L. Vinogradov, “Analog summ Akhiezera–Kreina–Favara dlya periodicheskikh splainov minimalnogo defekta”, Problemy mat. analiza, 25, 2003, 29–56 | MR | Zbl

[13] O. L. Vinogradov, “Tochnye neravenstva dlya priblizhenii klassov periodicheskikh svertok podprostranstvami sdvigov nechetnoi razmernosti”, Mat. zametki, 85:4 (2009), 569–584 | DOI | MR | Zbl