Estimates for solutions to neutral difference-differential equations (Q1589210)

The neutral functional-differential equation \[ \sum^m_0 (B_j u(t- h_j)+ D_j {d\over dt} u(t- h_j))= 0,\quad \dim u= n, \] \[ 0= h_0< h_1<\cdots< h_m= h, \] is considered. Exponential estimates for the solutions are obtained within the framework of spectral theory. The main feature of the paper is the property of the exponential solutions to the system to define a Riesz basis in the Sobolev space \(W^1_2(-h, 0; \mathbb{C}^n)\). The main nondegeneracy assumptions are \(\text{det }D_0\neq 0\), and \(\text{det }D_m\neq 0\).