Analysis of linear periodic operators and systems

Abstract

Let us have a linear operator

$$y(t) = \cup [x(t)]$$

(7.1)

with the PTF

$$W(s,t) = \cup [{{e}^{{st}}}]{{e}^{{ - st}}}$$

(7.2)

defined in the stripe α < Re s < β or in the half-plane Re s > α (in this case we take β = ∞). Assume that x(t) ∈ Λ (α, β) and

$$\begin{array}{*{20}{c}} {X(s) = \int_{{ - \infty }}^{\infty } {x(t){{e}^{{ - st}}}dt,} } & {\alpha < \operatorname{Re} s < \beta .} \\ \end{array}$$

(7.3)