Geodesic
Optimal Recovery of Harmonic Functions in the Ball from Inaccurate Information on the Radon Transform
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 163-172

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We consider the problem of the optimal recovery of harmonic functions in the ball from inaccurate information on the Radon transform. Presented are the error of the optimal recovery and the set of optimal methods for which this error is attained.
Keywords: optimal recovery, harmonic function, Hardy space, spherical harmonic, Lagrange function, Bessel function.
Mots-clés : Radon transform, Gegenbauer polynomial 
T. È. Bagramyan. Optimal Recovery of Harmonic Functions in the Ball from Inaccurate Information on the Radon Transform. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 163-172. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a0/
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[1] 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

[2] C. A. Micchelli, T. J. Rivlin, “Lectures on optimal recovery”, Numerical Analysis, Lecture Notes in Math., 1129, Springer-Verlag, Berlin, 1985, 21–93 | DOI | MR | Zbl

[3] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Optimalnoe vosstanovlenie operatorov po netochnoi informatsii”, Matematicheskii forum. T. 2. Issledovaniya po vypuklomu analizu, VNTs RAN, Vladikavkaz, 2009, 158–192

[4] K. Yu. Osipenko, “Optimalnaya interpolyatsiya analiticheskikh funktsii”, Matem. zametki, 12:4 (1972), 465–476 | MR | Zbl

[5] K. Y. Osipenko, M. I. Stessin, “Hadamard and Schwarz type theorems and optimal recovery in spaces of analytic functions”, Constr. Approx., 31:1 (2010), 37–67 | DOI | MR | Zbl

[6] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “O vosstanovlenii operatorov svertochnogo tipa po netochnoi informatsii”, Teoriya funktsii i differentsialnye uravneniya, Tr. MIAN, 269, MAIK, M., 2010, 181–192 | MR | Zbl

[7] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Ob optimalnom garmonicheskom sinteze po netochno zadannomu spektru”, Funkts. analiz i ego pril., 44:3 (2010), 76–79 | DOI | MR | Zbl

[8] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Neravenstvo Khardi–Littlvuda–Polia i vosstanovlenie proizvodnykh po netochnoi informatsii”, Dokl. RAN, 438:3 (2011), 300–302 | MR | Zbl

[9] F. Natterer, The Mathematics of Computerized Tomography, John Wiley Sons, Chichester, 1986 | MR | Zbl

[10] T. E. Bagramyan, “Optimalnoe vosstanovlenie garmonicheskoi funktsii po netochno zadannym znacheniyam operatora radialnogo integrirovaniya”, Vladikavk. matem. zhurn., 14:1 (2012), 22–36 | MR

[11] A. J. DeGraw, “Optimal recovery of holomorphic functions from inaccurate information about radial integration”, Amer. J. Comput. Math., 2 (2012), 258–268 | DOI

[12] S. Axler, P. Bourdon, W Ramey, Harmonic Function Theory, Grad. Texts in Math., 137, Springer-Verlag, New York, 2001 | DOI | MR | Zbl

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

[14] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Nauka, M., 1966 | MR | Zbl