Systems of advance-delay differential-difference equations and transformation groups - Serguei I. Iakovlev; Valentina Iakovleva (Electronic Journal of Differential Equations, 2016)
A linear system of mixed-type differential difference equations is studied. A step derivation method and some conditions on an initial function are used to guarantee existence, uniqueness and smoothness of the solution. Further, a transformation group is defined on a complete countably normed space of initial functions and the spectrum of the infinitesimal generator of this group is studied. The same technique applies to a linear system of retarded differential difference equations. A problem to extend solutions of such a system to the left on the real line is solved.