An application of the theory of positive operators in the investigation of rough properties of linear differential systems (Q2761401)

The author deals with the system of linear differential equations NEWLINE\[NEWLINE \dot x = A(t)x,\quad x\in \mathbb{R}^n,\tag{1} NEWLINE\]NEWLINE where \(A(\cdot): \mathbb{R}\to\text{End} (\mathbb{R}^n,\mathbb{R}^n)\) is a continuous and bounded mapping, \(t\geq 0\). He introduces and studies conditions for the weak exponential separability of system (1). The theorems proved in the paper imply that system (1) with an almost-periodic matrix is either exponentially separable with some index or uniformly nonseparable.