A new approach to asymptotic diagonalization of linear differential systems
The authors study the asymptotic diagonalization of systems \[ \dot{x} = [\Lambda(t) + P(t) + R(t)]x \quad \text{in } \mathbb{R}^n \] where \(\Lambda\) is an \(L_{\text{loc}}^p\)-matrix, \(P\) is \(L^m\) and \(R\) is \(L^1\), \(p,m \in [1,\infty)\). Using linear skew-product flows and spectral theory, the authors show that if the unperturbed system \[ \dot{x} = \Lambda(t) x \] has full spectrum (i.e. \(n\) spectral intervals) over its hull, then the entire system is asymptotically diagonalizable almost everywhere.
scientific article; zbMATH DE number 1453232