Geodesic
Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error
Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 163-170.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: analytic function, optimal recovery, extremal problem. 
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R. R. Akopian. Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error. Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 163-170. http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a0/

[1] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950 | MR | Zbl

[2] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Gostekhizdat, M.–L., 1952 | MR | Zbl

[3] F. Nevanlinna, R. Nevanlinna, “Über die Eigenschaften einer analytischen Funktionen in der Umgeburg einer singularen Stille oder Linie”, Acta Soc. Sc. Fennicae, 50:5 (1922), 1–46 | Zbl

[4] V. V. Arestov, “O ravnomernoi regulyarizatsii zadachi vychisleniya znachenii operatora”, Matem. zametki, 22:2 (1977), 231–244 | MR | Zbl

[5] C. A. Micchelli, T. J. Rivlin, “A survey of optimal recovery”, Optimal Estimation in Approximation Theory, Plenum Press, New York, 1977, 1–54 | MR | Zbl

[6] V. V. Arestov, “Nailuchshee vosstanovlenie operatorov i rodstvennye zadachi”, Sbornik trudov Vsesoyuznoi shkoly po teorii funktsii (Dushanbe, avgust 1986 g.), Tr. MIAN SSSR, 189, Nauka, M., 1989, 3–20 | MR

[7] V. V. Arestov, V. N. Gabushin, “Nailuchshee priblizhenie neogranichennykh operatorov ogranichennymi”, Izv. vuzov. Matem., 1995, no. 11, 42–68 | MR | Zbl

[8] V. V. Arestov, “Priblizhenie neogranichennykh operatorov ogranichennymi i rodstvennye ekstremalnye zadachi”, UMN, 51:6 (1996), 89–124 | DOI | MR | Zbl

[9] K. Yu. Osipenko, Optimal Recovery of Analytic Functions, NJVA Science Publ., Huntington, 2000

[10] V. N. Gabushin, “Nailuchshee priblizhenie funktsionalov na nekotorykh mnozhestvakh”, Matem. zametki, 8:5 (1970), 551–562 | MR | Zbl

[11] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Ob optimalnom vosstanovlenii funktsionalov po netochnym dannym”, Matem. zametki, 50:6 (1991), 85–93 | MR | Zbl

[12] S. B. Stechkin, “Neravenstva mezhdu normami proizvodnykh proizvolnoi funktsii”, Acta Sci. Math., 26:3-4 (1965), 225–230 | Zbl

[13] S. B. Stechkin, “Nailuchshee priblizhenie lineinykh operatorov”, Matem. zametki, 1:2 (1967), 137–148 | MR | Zbl

[14] G. M. Goluzin, V. I. Krylov, “Obobschennaya formula Carleman'a i prilozhenie ee k analiticheskomu prodolzheniyu funktsii”, Matem. sb., 40:2 (1933), 144–149 | Zbl

[15] L. A. Aizenberg, Formuly Karlemana v kompleksnom analize. Pervye prilozheniya, Nauka, Novosibirsk, 1990 | MR | Zbl

[16] M. M. Lavrentev, V. G. Romanov, S. P. Shishatskii, Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR | Zbl

[17] R. R. Akopyan, “Nailuchshee priblizhenie operatora analiticheskogo prodolzheniya na klasse analiticheskikh v polose funktsii”, Tr. IMM UrO RAN, 17, no. 3, 2011, 46–54

[18] R. R. Akopyan, “Nailuchshee priblizhenie operatora analiticheskogo prodolzheniya na klasse analiticheskikh v koltse funktsii”, Tr. IMM UrO RAN, 18, no. 4, 2012, 3–13