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

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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/}
}
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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/