Upper and lower estimates for rate of convergence in the Chernoff product formula for semigroups of operators
摘要
This paper studies the rates of convergence of Chernoff approximations to operator semigroups. We show that the convergence, in general, can be arbitrarily fast or arbitrarily slow. Under natural assumptions, the main result provides an upper estimate for the convergence rates. As an illustration, the result is applied to the study of Chernoff approximations for solutions of one-dimensional parabolic differential equations with variable coefficients.