Polynomial approximation to the solution of the cauchy problem

The Cauchy problem for a nonhomogeneous first-order differential-operator equation of parabolic type in a Hilbert space is considered. Polynomial approximations and estimates of their convergence are obtained which depend on the character of the right-hand side and the initial conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 427–429, March, 1991.