Determinants and Periodic Solutions of Delay Equations

Finite difference equations may be thought of as discrete analogues of delay equations. Taking this point of view, we give an elementary account of an algebraic determinant identity, due to Burghelea, Friedlander and Kappeler, which relates the determinant of a periodic difference operator to the monodromy of a fundamental solution. The result is applied to a simple class of functional integral operators. (c) 2005 Elsevier Inc. All rights reserved.