The generalized Green operator of an overdetermined boundary value problem for a linear functional-differential equation (Q1901916)

The author considers a linear abstract functional differential equation (1) \({\mathcal L} x = f\) where \({\mathcal L}\) is a linear operator acting from a Banach space \({\mathcal D}\) into a Banach space \(B\) and \({\mathcal D}\) is isomorphic to \(B \times R^n\), together with boundary conditions (2) \(lx = \alpha\) where \(l = [l^1, \dots, l^N] : {\mathcal D} \to R^N\) is a linear bounded vector functional with linearly independent components. In the case where \(N > n\), i.e. the boundary value problem (1), (2) is overdetermined, she constructs an extended problem which is uniquely solvable.