Geodesic
Optimal recovery of semi-group operators from inaccurate data
Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 75-84.

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

The problem of optimal recovery of the operator at a given value of the parameter from inaccurate information about the other parameters is solved for a special one-parameter semi-group of operators. A family of optimal recovery methods is constructed. As a corollary, we obtain families of optimal recovery methods in the problem of recovery of a solution of the heat equation on the line and in the problem of recovery of a solution to the Dirichlet problem for the half-plane. 
@article{EMJ_2019_10_4_a7,
     author = {G. G. Magaril-Il'yaev and E. O. Sivkova},
     title = {Optimal recovery of semi-group operators from inaccurate data},
     journal = {Eurasian mathematical journal},
     pages = {75--84},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a7/}
}
TY  - JOUR
AU  - G. G. Magaril-Il'yaev
AU  - E. O. Sivkova
TI  - Optimal recovery of semi-group operators from inaccurate data
JO  - Eurasian mathematical journal
PY  - 2019
SP  - 75
EP  - 84
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a7/
LA  - en
ID  - EMJ_2019_10_4_a7
ER  - 
%0 Journal Article
%A G. G. Magaril-Il'yaev
%A E. O. Sivkova
%T Optimal recovery of semi-group operators from inaccurate data
%J Eurasian mathematical journal
%D 2019
%P 75-84
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a7/
%G en
%F EMJ_2019_10_4_a7
G. G. Magaril-Il'yaev; E. O. Sivkova. Optimal recovery of semi-group operators from inaccurate data. Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 75-84. http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a7/

[1] E. V. Abramova, “On optimal recovery of Dirichlet problem from a boundary function known approximately”, Vladikavkaz. Mat. Zh., 17:1 (2015), 3–13 | MR

[2] E. A. Balova, “Optimal reconstruction of the solution of the Dirichlet problem from inaccurate input data”, Math. Notes, 82 (2007), 285–294 | DOI | MR | Zbl

[3] A. N. Kolmogorov, S. V. Fomin, Elements of theory of functions and functional analysis, Dover, Mineola, NY, 1999 | MR

[4] G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of functions and their derivatives from inaccurate information about the spectrum and inequalities for derivatives”, Funct. Anal. Appl., 37 (2003), 203–214 | DOI | MR | Zbl

[5] G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682 | DOI | MR | Zbl

[6] G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185 | DOI | MR | Zbl

[7] G. G. Magaril-Il'yaev, K. Yu. Osipenko, V. M. Tikhomirov, “On optimal recovery of heat equation solutions”, Approximation Theory, A volume dedicated to B. Bojanov, eds. D.K. Dimitrov, G. Nikolov, R. Uluchev, Marin Drinov Acad. Publ. House, Sofia, 2004, 163–175 | MR

[8] G. G. Magaril-Il'yaev, E. O. Sivkova, “Best recovery of the Laplace operator of a function from incomplete spectral data”, Sb. Math., 203:4 (2012), 569–580 | DOI | MR | Zbl

[9] G. G. Magaril-Il'yaev, V. M. Tikhomirov, Convex analysis: theory and applications, Am. Math. Soc., Providence, RI, 2003 | MR | Zbl

[10] A. A. Melkman, C. A. Micchelli, “Optimal estimation of linear operators in Hilbert spaces from inaccurate data”, SIAM J. Numer. Anal., 16 (1979), 87–105 | DOI | MR | Zbl

[11] E. M. Stein, G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, 1971 | MR | Zbl