On the Recovery of Semi-group Operators in Weight Spaces from Incomplete and Inaccurate Data

The paper is devoted to the problem of recovery of the value of an operator from a one-parameter semigroup on elements of weighted functional spaces. It is assumed that the action of the semigroup operators is approximately known for two different parameter values (measurement results) and it is necessary to recover the action of the semigroup operator for a fixed parameter value between these values. The concepts of the recovery method, the errors of the recovery method, the optimal recovery method, and the errors of the optimal recovery method are introduced. A family of optimal recovery methods has been constructed.