Spectral conditions for admissibility of evolution equations in Hilbert space (Q2371863)

The author considers the question of regular admissibility for general functional-differential equations of the form \[ u^{\prime} (t)= \left({\mathcal B}u\right)(t) + f(t) \] where \({\mathcal B}\) is a closable densely defined operator acting on the space of almost periodic \(H\)-valued functions. The method is based on the spectral properties of sums of cummuting operators. The author provides some very useful applications.