Optimal extrapolation of polynomials given with error

The problem of optimal extrapolation of polynomials given with an error on a compact set is studied. Its relationship with Chebyshev's problem on a polynomial that least deviates from zero on a compact set is established. An exact solution to the problem of optimal extrapolation of polynomials is obtained for the case when the compact set is a lemniscate. An exact solution is written for the problem of extrapolation from the interval $[-1,1]$ to the real line.