Geodesic
Sharp estimates of best approximations in terms of holomorphic functions of Weierstrass-type operators
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 18-60
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We establish the estimates $$ A_\sigma(f)_P\le KP\bigl(\Phi(\mathcal W)f\bigr), $$ where $W$ is a kernel of special type summable on $\mathbb R$, a function $\Phi$ is holomorphic in the neighborhood of the spectrum of $W$, $A_\sigma(f)_P$ is the best approximation of a function $f$ by entire functions of exponential type not greater than $\sigma$, with respect to seminorm $P$. In some cases 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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     title = {Sharp estimates of best approximations in terms of holomorphic functions of {Weierstrass-type} operators},
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O. L. Vinogradov. Sharp estimates of best approximations in terms of holomorphic functions of Weierstrass-type operators. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 18-60. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a1/

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

[2] O. L. Vinogradov, “Tochnye neravenstva tipa Dzheksona dlya priblizhenii klassov svertok tselymi funktsiyami konechnoi stepeni”, Algebra i analiz, 17:4 (2005), 56–114 | MR | Zbl

[3] O. L. Vinogradov, “Tochnye otsenki nailuchshikh priblizhenii cherez otkloneniya integralov tipa Veiershtrassa”, Zap. nauchn. semin. POMI, 401, 2012, 53–70 | MR

[4] B. M. Makarov, M. G. Goluzina, A. A. Lodkin, A. N. Podkorytov, Izbrannye zadachi po veschestvennomu analizu, SPb., 2004 | MR

[5] A. G. Babenko, Yu. V. Kryakin, “Integralnoe priblizhenie kharakteristicheskoi funktsii intervala i neravenstvo Dzheksona v $C(\mathbb T)$”, Trudy IMM UrO RAN, 15, no. 1, 2009, 59–65

[6] 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

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

[8] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, M., 1960

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

[10] I. F. Stefensen, Teoriya interpolyatsii, M.–L., 1935

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

[12] V. V. Zhuk, Approksimatsiya periodicheskikh funktsii, L., 1982 | MR

[13] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, M., 1963