Characteristic Matrix Functions and Periodic Delay Equations

Abstract

In the first part of this chapter we recall the notion of a characteristic matrix function for classes of operators as introduced in Kaashoek and Verduyn Lunel (2023). The characteristic matrix function completely describes the spectral properties of the corresponding operator. In the second part we show that the period map or monodromy operator associated with a periodic neutral delay equation has a characteristic matrix function. We end this chapter with a number of illustrative examples of periodic neutral delay equations for which we can compute the characteristic matrix function explicitly.