We develop the theory of compound functional differential equations, which
are tensor and exterior products of linear functional differential equations.
Of particular interest is the equation x˙(t)=−α(t)x(t)−β(t)x(t−1) with a single delay, where the delay
coefficient is of one sign, say δβ(t)≥0 with δ∈−1,1.
Positivity properties are studied, with the result that if (−1)k=δ then
the k-fold exterior product of the above system generates a linear process
which is positive with respect to a certain cone in the phase space.
Additionally, if the coefficients α(t) and β(t) are periodic of
the same period, and β(t) satisfies a uniform sign condition, then there
is an infinite set of Floquet multipliers which are complete with respect to an
associated lap number. Finally, the concept of u0​-positivity of the exterior
product is investigated when β(t) satisfies a uniform sign condition.Comment: 84 page