Fréchet differentiability of parameter-dependent analytic semigroups (Q1284514)

The authors study dependence on a vector-valued parameter \(q\) of a collection of analytic semigroups \(\{T(t;q), t\geq 0\}\). The analyticity of the map \(q\mapsto T(t;q)\) in the uniform operator topology is established and, moreover, the Fréchet derivative of \(T(t;q)\) with respect to \(q\) is given by a norm-convergent contour integral.