Geodesic
Sharp estimates of best approximations by deviations of Weierstrass-type integrals
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 53-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish the estimates $$ A_\sigma(f)_P\le KP(f-f*W), $$ where $W$ is a kernel of special type summable on $\mathbb R$ and $A_\sigma(f)_P$ is the best approximation (with respect to a seminorm $P$) of a function $f$ by entire functions of exponential type not greater than $\sigma$. For the uniform and the integral norm we find the least possible constant $K$. The estimates are obtained by linear methods of approximation. 
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     author = {O. L. Vinogradov},
     title = {Sharp estimates of best approximations by deviations of {Weierstrass-type} integrals},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a1/}
}
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O. L. Vinogradov. Sharp estimates of best approximations by deviations of Weierstrass-type integrals. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 53-70. http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a1/

[1] N. I. Akhiezer, Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR | Zbl

[2] V. V. Zhuk, Approksimatsiya periodicheskikh funktsii, Izd-vo LGU, L., 1982 | MR | Zbl

[3] 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

[4] V. P. Zastavnyi, V. V. Savchuk, “Priblizheniya klassov svertok lineinymi operatorami spetsialnogo vida”, Matem. zam., 90:3 (2011), 351–361 | DOI | MR | Zbl

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

[6] D. V. Widder, The Laplace Transform, Princeton, 1946

[7] E. Kamke, Integral Lebega–Stiltesa, GIFML, M., 1959