Time-Dependent Product Formulæ: Hilbert Space

In this chapter we present the product-formula approximations of solution operator for non-autonomous Cauchy problem (nACP) in a Hilbert space. Under a similar to Chap. 11 the infinitesimal smallness and time-continuity conditions on perturbation in the nACP, the product approximation can be established within such approach in the operator-norm topology, but with (in a certain sense) better estimate for the bound of the rate of convergence. The latter is essentially due to a supplementary condition of the self-adjointness.