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DOI: 10.23671/VNC.2015.1.7285
On optimal recovery of dirichlet problem from a boundary function known approximately
Abramova E. V.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 1.
Abstract: The problem of best (optimal) recovery of a solution of the Dirichlet problem for the upper half-plane from the Fourier transform of the boundary functions known approximately in considered. A series of optimal recovery methods are foud and the corresponding errors recovery are calculated.
For citation: Abramova E. V. On optimal recovery of dirichlet problem from a boundary function known approximately. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 1, pp.3-13. DOI 10.23671/VNC.2015.1.7285
1. Smoljak S. A. Ob Optimal'nom Vosstanovlenii Funkcij i
Funkcionalov ot Nih: Diss. ... k.f.-m.n., Moskva, Moskovskii Gos.
Univ., 1965 (Russian).
2. Marchuk A. G., Osipenko K. Ju. Best Approximation of Functions
Specified with an Error at a Finite Number of Points. Mathematical
Notes [Matematicheskie Zametki, 1975, vol. 17, no. 3, pp. 359-368],
1975, vol. 17, no. 3, pp. 207-212.
3. Micchelli C. A., Rivlin T. J. A Survey of Optimal Recovery.
Optimal Estimation in Approximation Theory, N.Y., Plenum Press,
1977, pp. 1-54.
4. Melkman A. A., Micchelli C. A. Optimal Estimation of Linear
Operators in Hilbert Spaces from Inaccurate Data. SIAM J. Numer.
Anal., 1979, pp. 87-105.
5. Micchelli C. A., Rivlin T. J. Lectures on Optimal Recovery.
Lecture Notes in Mathematics, Berlin, Springer, 1985, vol. 1129,
pp.21-93.
6. Magaril-Il'jaev G. G., Osipenko K. Ju. Optimal Recovery of
Functions and Their Derivatives from Inaccurate Information about
the Spectrum and Inequalities for Derivatives. Functional Analysis
and Its Applications [Funkcional'nyi Analiz i Ego Prilozheniya,
2003, vol. 37, no. 3, pp. 51-64], 2003, vol. 37, no. 3, pp. 203-214.
7. Magaril-Il'jaev G. G., Osipenko K. Ju. On the Reconstruction of
Convolution-Type Operators from Inaccurate Information. Proceedings
of the Steklov Institute of Mathematics [Trudy MIAN, 2010, vol.269,
no. 1, pp. 181-192], 2010, vol.269, no. 1, pp. 174-185.
8. Magaril-Il'jaev G. G., Osipenko K. Ju. On Optimal Harmonic
Synthesis from Inaccurate Spectral Data. Functional Analysis and Its
Applications [Funkcional'nyi Analiz I Ego Prilozheniya, 2010, vol.
44, no. 3, pp. 76-79], 2010, vol.44, pp.223-225.
9. Stejn I. Vejs G. Vvedenie v Garmonicheskij Analiz na Evklidovyh
Prostranstvah, Moskva, 1974 (Russian).
10. Magaril-Il'jaev G. G., Tihomirov V. M. Vypuklyj Analiz i Ego
Prilozhenija (3-e izd.), Moskva, Editorial URSS, 2011 (Russian).
11. Kolmogorov A. N., Fomin S. V. Elementy Teorii Funkcij I
Funkcional'nogo Analiza (4-e izd.), Moskva, Nauka, 1976 (Russian).
