Holomorphic \(C\)-existence families (Q1201457)

Generalizing the concept of strongly continuous semigroups, \(C\)-existence families of semigroups were introduced in connection with the abstract Cauchy problem \[ u'(t,x)= A\bigl(u(t,x)\bigr),\quad t\geq 0,\quad u(0,x)=x. \] In this paper, the author defines the holomorphic \(C\)- continuous families so as to generalize holomorphic strongly continuous semigroups. They also generalize the Hille-Yosida type characterizations of densely defined generators of holomorphic strongly continuous semigroups.