Differential systems with reflection and matrix invariants

Abstract

In this work, we derive important properties regarding matrix invariants that occur in the theory of differential equations with reflection.

A Liouville’s Formula for Systems with Reflection

“…There has also been a search for Hilbert bases related to operator eigenfunction decompositions [6,7] and explicit solutions or the associated Green's functions [8][9][10][11][12][13]. Many of these works highlight the strong relation between linear analysis and linear algebra, either in the context of ordinary differential equations [10,12], systems [13,14], difference equations [15] or partial differential equations [16]. In particular, in [13], the authors developed an explicit fundamental matrix for the system of differential equations with reflection:…”