A multiplicity theorem for hyperbolic systems (Q1822680)

Certain hyperbolic systems in one space variable, including retarded functional differential equations, are rewritten as abstract evolution equations \(dw/dt=Aw\). The characteristic equation \(h(\lambda)=0\) of all such equations is computed and it is shown, by a rather explicit computation, that the range of the spectral projection, i.e. the dimension of the kernel of \((\lambda_ 0I-A)^ m\), equals m, where m is the multiplicity of \(\lambda_ 0\) as a root of \(h(\lambda)=0\). The results extend those of \textit{B. W. Levinger} [J. Differ. Equations 4, 612-619 (1968; Zbl 0174.139)].