Reducibility of linear dynamic equations on measure chains (Q1602831)

The authors generalize the concepts of reducibility and kinematic similarity to the case of dynamic equations in Hilbert spaces. In this context they provide sufficient and necessary conditions for certain systems to be transformable into systems of a simpler form: Restrictively stable systems \(\to\) zero systems, RS-decomposable systems \(\to\) Hermitian systems, dichotomous systems \(\to\) systems with block diagonal structure. Throughout the paper the effects of the underlying measure chain structure and of certain features of operator theory to the whole theory are discussed.