Optimal recovery of semi-group operators from inaccurate data - Magaril-Il’yaev, Georgii; Sivkova, Elena (Eurasian Mathematical Journal, 2019)
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.