Geodesic
Optimal recovery of a harmonic function from inaccurate information on the values of the radial integration operator
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 1, pp. 22-36 
T. Bagramyan. Optimal recovery of a harmonic function from inaccurate information on the values of the radial integration operator. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 1, pp. 22-36. http://geodesic.mathdoc.fr/item/VMJ_2012_14_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of optimal recovery of a harmonic function in the unit ball from the inaccurate values of the radial integration operator. Information on the values of the operator is given as a function that differs from the exact values in the mean-square metric not more than a fixed error, either in the form of a finite set of Fourier coefficients calculated with a fixed error in the mean square or uniform metric.

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

[2] Michelli A., Rivlin T. J., “Lectures on optimal recovery”, Numerical analysis (Lancaster, 1984), Lecture Notes in Math., 1129, Springer-Verlag, Berlin, 1985, 21–93 | DOI | MR

[3] Magaril-Ilyaev G. G., Osipenko K. Yu., “Optimalnoe vosstanovlenie operatorov po netochnoi informatsii”, Mat. forum, v. 2, Itogi nauki. Yuzhnyi federalnyi okrug, Issledovaniya po vypuklomu analizu, VNTs RAN, Vladikavkaz, 2009, 158–192

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

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

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

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

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

[9] Natterer F., The mathematics of computerized tomography, John Wiley Sons, Stuttgart, 1986, 222 pp. | MR | Zbl

[10] Axler S., Bourdon P., Ramey W., Harmonic function theory, Second edition, Springer-Verlag, New York, 2001, 270 pp. | MR | Zbl