Geodesic
Informativeness of all the linear functionals in the recovery of
Sbornik. Mathematics, Tome 198 (2007) no. 11, pp. 1535-1551 Cet article a éte moissonné depuis la source Math-Net.Ru

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The informativeness of all the linear functionals in the recovery of functions in the classes $H_p^\omega$ is investigated. The optimal recovery orders of functions in $H_p^\omega$ are found. These are completely determined by embedding theorems, similarly to the case of function classes with smoothness described in terms of numerical parameters. Bibliography: 28 titles. 
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Sh. U. Azhgaliev; N. Temirgaliev. Informativeness of all the linear functionals in the recovery of. Sbornik. Mathematics, Tome 198 (2007) no. 11, pp. 1535-1551. http://geodesic.mathdoc.fr/item/SM_2007_198_11_a0/

[1] V. M. Tikhomirov, Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976 | MR

[2] K. I. Babenko, Osnovy chislennogo analiza, Nauka, M., 1986 | MR | Zbl

[3] V. N. Temlyakov, Approximation of functions with bounded mixed derivative, Proc. Steklov Inst. Math., 178, 1989 | MR | MR | Zbl | Zbl

[4] N. Korneĭchuk, Exact constants in approximation theory, Encyclopedia Math. Appl., 38, Cambridge Univ. Press, Cambridge, 1991 | MR | MR | Zbl | Zbl

[5] K. Yu. Osipenko, “On $n$-widths, optimal quadrature formulas, and optimal recovery of functions analytic in a strip”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 55–78 | DOI | MR | Zbl

[6] K. Yu. Osipenko, K. Wilderotter, “Optimal information for approximating periodic analytic functions”, Math. Comp., 66:220 (1997), 1579–1592 | DOI | MR | Zbl

[7] S. D. Fisher, Ch. A. Micchelli, “Optimal sampling of holomorphic functions”, Amer. J. Math., 106:3 (1984), 593–609 | DOI | MR | Zbl

[8] S. D. Fisher, Ch. A. Micchelli, “Optimal sampling of holomorphic functions. II”, Math. Ann., 273:1 (1985), 131–147 | DOI | MR | Zbl

[9] N. Temirgaliev, “Teoretiko-chislovye metody i teoretiko-veroyatnostnyi podkhod k zadacham analiza. Teoriya vlozhenii i priblizhenii, absolyutnaya skhodimost i preobrazovaniya ryadov Fure”, Vestn. Evraz. un-ta, 1997, no. 3, 90–144 | MR

[10] Sh. Azhgaliev, N. Temirgaliev, “Informativeness of linear functionals”, Math. Notes, 73:5–6 (2003), 759–768 | DOI | MR | Zbl

[11] N. Temirgaliev, “Teoretiko-chislovye metody i teoretiko-veroyatnostnyi podkhod k zadacham analiza. Teoriya vlozhenii i priblizhenii, absolyutnaya skhodimost i preobrazovaniya ryadov Fure (Prodolzhenie 1)”, Vestn. Evraz. nats. un-ta, 3–4 (2002), 222–272

[12] N. Temirgaliev, “Problemy teorii funktsii i vychislitelnye metody (doklad, predstavlennyi na Vsemirnyi Kongress matematikov 2006 goda v Madride)”, Vestn. Evraz. nats. un-ta, 2 (2007), 19–51

[13] P. L. Ul'janov, “The imbedding of certain function classes $H_p^\omega$”, Math. USSR-Izv., 2:3 (1968), 601–637 | DOI | MR | Zbl | Zbl

[14] P. L. Ul'yanov, “Absolute and uniform convergence of Fourier series”, Math. USSR-Sb., 1 (1967), 169–197 | DOI | MR | Zbl

[15] Teoriya funktsii i vychislitelnye metody, Materialy Mezhdunarodnoi konf., posvyaschennoi 60-letiyu so dnya rozhdeniya prof. N. Temirgalieva (Astana, 2007), Izd-vo ENU, Astana, 2007 | Zbl

[16] K. I. Oskolkov, “Inequalities of the “large sieve” type and applications to problems of trigonometric approximation”, Anal. Math., 12:2 (1986), 143–166 | DOI | MR | Zbl

[17] V. N. Temlyakov, “Approximate recovery of periodic functions of several variables”, Math. USSR-Sb., 56:1 (1987), 249–261 | DOI | MR | Zbl

[18] V. Kh. Khristov, “O skhodimosti nekotorykh interpolyatsionnykh protsessov v integralnykh i diskretnykh normakh”, Konstruktivnaya teoriya funktsii (Varna, 1981), Izd-vo AN Bolgarii, Sofiya, 1983, 185–188 | MR | Zbl

[19] K. G. Ivanov, “On the rates of convergence of two moduli of functions”, Pliska Stud. Math. Bulgar., 5 (1983), 97–104 | MR | Zbl

[20] S. N. Kudryavtsev, “Some problems in approximation theory for a class of functions of finite smoothness”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 145–164 | DOI | MR | Zbl | Zbl

[21] P. L. Ulyanov, “O ryadakh po sisteme Khaara”, Matem. sb., 63(105):3 (1964), 356–391 | MR | Zbl

[22] A. V. Efimov, “Lineinye metody priblizheniya nepreryvnykh periodicheskikh funktsii”, Matem. sb., 54(96):1 (1961), 51–90 | MR | Zbl

[23] B. Szökefalvi-Nagy, “Approximation properties of orthogonal expansion”, Acta Sci. Math. (Szeged), 15:1 (1953), 31–37 | MR | Zbl

[24] V. A. Andrienko, “The imbedding of certain classes of functions”, Math. USSR-Izv., 1:6 (1967), 1255–1270 | DOI | MR | MR | Zbl

[25] V. A. Andrienko, “Necessary conditions for imbedding the function classes $H_p^\omega$”, Math. USSR-Sb., 7:2 (1969), 273–292 | DOI | MR | Zbl | Zbl

[26] S. M. Nikol'skiĭ, Approximation of functions of several variables and imbedding theorems, Springer-Verlag, Berlin–Heidelberg–New York, 1975 | MR | MR | Zbl | Zbl

[27] A. Kurosh, Higher algebra, Mir, Moscow, 1988 | MR | MR | Zbl

[28] A. F. Timan, Theory of approximation of functions of a real variable, Pergamon, New York, 1963 | MR | MR | Zbl