Completeness Theorems for Period Maps

Abstract

We consider completeness problems for period maps associated with periodic functional differential equations. These maps are bounded linear operators acting on Banach spaces of continuous functions. In the first section we show that these period maps are compact operators which can be written as the sum of a Volterra operator and a finite rank operator. The significance of completeness theorems for period maps is explained in the second and third section. Two completeness theorems for the period map of certain concrete scalar periodic delay equations are presented in the fourth and the fifth section, first for one-periodic equations and next for two-periodic equations.