Reducibility of linear dynamic equations on measure chains

The concepts of reducibility and kinematic similarity are of major significance in the theory of stability of linear differential and difference equations. In this paper we generalize some fundamental results on reducibility from the finite-dimensional differential equations context to dynamic equations on measure chains in arbitrary Hilbert spaces. In fact, we derive sufficient conditions for dynamic equations to be kinematically similar to an equation with zero right-hand side or to an equation in Hermitian or block diagonal form.