Optimal recovery of analytic functions from boundary conditions specified with error

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• 作者：R. R. Akopyan
• 关键词：analytic function ; optimal recovery ; extremal problem
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：99
• 期：1-2
• 页码：177-182
• 全文大小：602 KB
• 参考文献：1.I. I. Privalov, Boundary Properties of Analytic Functions (Gosudarstv. Izdat. Tekhn.-Teor. Lit., Moscow–Leningrad, 1950) [in Russian].
  2.G. M. Goluzin, Geometric Theory of Functions of a Complex Variable (Gostekhizdat, Moscow–Leningrad, 1952; AmericanMathematical Society, Providence, RI, 1969).MATH
  3.F. Nevanlinna and R. Nevanlinna, “Über die Eigenschaften einer analytischen Funktionen in der Umgeburg einer singularen Stille oder Linie,” Acta Soc. Sc. Fennicae 50 (5), 1–46 (1922).MathSciNet MATH
  4.V. V. Arestov, “The uniform regularization of the problem of computing the values of an operator,” Mat. Zametki 22 (2), 231–244 (1977) [in Russian].MathSciNet
  5.C. A. Micchelli and T. J. Rivlin, “A survey of optimal recovery,” in Optimal Estimation in Approximation Theory (Plenum Press, New York, 1977), pp. 1–54.
  6.V. V. Arestov, “Optimal recovery of operators and related problems,” in Trudy Mat. Inst. Steklov, Vol. 189: Collection of Papers from the All-Union School on the Theory of Functions, Dushanbe, Aug. 1986 (Nauka, Moscow, 1989), pp. 3–20 [Proc. Steklov Inst. Math. No. 4, 1–20 (1990)].MathSciNet
  7.V. V. Arestov and V. N. Gabushin, “Best approximation of unbounded operators by bounded operators,” Izv. Vyssh. Uchebn. Zaved. Mat. (11), 42–68 (1995) [RussianMath. (Iz. VUZ) 39 (11). 38–63 (1995) (1996)].MathSciNet MATH
  8.V. V. Arestov, “Approximation of unbounded operators by bounded ones, and related extremal problems,” UspekhiMat. Nauk 51 (6), 89–124 (1996) [Russ.Math. Surv. 51 (6), 1093–1126 (1996)].MathSciNet CrossRef
  9.K. Yu. Osipenko, Optimal Recovery of Analytic Functions (NJVA Science Publ., Huntington, 2000).
  10.V. N. Gabushin, “Best approximations of functionals on certain sets,” Mat. Zametki 8 (5), 551–562 (1970) [Math. Notes 8 (5), 780–785 (1970) (1971)].MathSciNet
  11.G. G. Magaril-Il’yaev and K. Yu. Osipenko, “Optimal reconstruction of functionals from inaccurate data,” Mat. Zametki 50 (6), 85–93 (1991) [Math. Notes 50 (5–6), 1274–1279 (1991)].MathSciNet MATH
  12.S. B. Stechkin, “Inequalities between norms of derivatives of an arbitrary function,” Acta Sci. Math. 26 (No. 3–4), 225–230 (1965).MathSciNet
  13.S. B. Stechkin, “Best approximation of linear operators,” Mat. Zametki 1 (2), 137–148 (1967) [Math. Notes 1 (1–2), 91–99 (1967) (1968)].MathSciNet MATH
  14.G. M. Goluzin and V. I. Krylov, “Generalized Carleman’s formula and its application to analytic continuation of functions,” Mat. Sb. 40 (2), 144–149 (1933).
  15.L. A. Aizenberg, Carleman Formulas in Complex Analysis: First Applications (Nauka Sibirsk. Otdel., Novosibirsk, 1990; Carleman’s Formulas in Complex Analysis: Theory and Applications, Kluwer, Dordrecht, 1993).CrossRef
  16.M. M. Lavrent’ev, V.G. Romanov, and S. P. Shishatskii, Ill-Posed Problems ofMathematical Physics and Analysis (Nauka, Moscow, 1980; AmericanMathematical Society, Providence, RI, 1986).
  17.R. R. Akopyan, “Best approximation of the operator of analytic continuation on the class of functions analytic in a strip,” in Trudy Inst. Mat. i Mekh. UrO RAN (2011), Vol. 17 (3), pp. 46–54.MathSciNet
  18.R. R. Akopyan, “Best approximation for the analytic continuation operator on the class of analytic functions in a ring,” in Trudy Inst. Mat. i Mekh. UrO RAN (2012), Vol. 18, pp. 3–13.
  
• 作者单位：R. R. Akopyan (1) (2)
  
  1. Ozersk Technology Institute, National Research Nuclear University “MIFI”, Ozersk, Chelyabinskaya Obl., Russia
  2. Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

The problem of optimal recovery of an analytic function from its values specified with error on a part of the boundary is solved, together with related extremal problems.