Optimal recovery: theory and applications

The talk will be devoted to the main results of optimal recovery theory of linear functionals and operators on classes of elements from inaccurate information about these elements (existence of linear methods of recovery, connection with adaptive algorithms, optimal recovery and extremal theory, etc.). In addition, the examples of optimal recovery for solutions of differentional and difference equations from inaccurate initial data and optimal recovery of signals from inaccurate spectrum will be given.