In this paper we apply a set-up introduced by R. K. Miller to transform a linear, inhomogeneous Cauchy problem for the generator of a semigroup on a Banach space into a homogeneous one for a matrix operator, which is the generator of a semigroup on a suitable product space. By using restriction theorems and extrapolation spaces we obtain new results for the inhomogeneous Cauchy problem for Hille-Yosida operators in Favard spaces.
"The Miller scheme in semigroup theory." Adv. Differential Equations 9 (3-4) 387 - 414, 2004.