Inhomogeneous semigroups of commuting operators

The concepts of the homogeneously continuable semigroup of operators, and of infinitesimal and reproducing families of a semigroup, are introduced. The class of strongly continuous homogeneously continuable semigroups of commuting linear operators is discussed. This class contains in particular the class $(C_0)$ of homogeneous semigroups. An analog of the Hill–Yosida theorem is proved for it.