Analytic semigroups with kernel and linear equations of Sobolev type (Q1921853)

Let \(U\) and \(F\) be Banach spaces, \(L\in{\mathcal L}(U,F)\) a bounded operator and \(M\) a densely defined closed operator on \(U\) with values in \(F\). The authors studies the following linear equation of Sobolev type \[ L\dot u= Mu. \] They determine conditions under which for a gaiven pair of analytic semigroups of operators with kernels there exists a pair of operators \(L\) and \(M\) generating these semigroups.