Spectral properties of some linear matrix differential operators in \(L^p\)-spaces on \({\mathbb{R}}\) (Q2480713)

The paper deals with a higher order matrix ordinary linear differential operator \[ T=\sum_0^n a_k(x) D^k,\quad x\in \mathbb{R},\;n\geq 2, \] in the space \(L^p(\mathbb{R}, \mathbb{C}^n)\) \((1 < p < \infty)\). The authors study it as a perturbation of a constant coefficient differential operator of order \(n\) by a lower order differential operator \(S\) which has a factorisation \(S = AB\) for suitable operators \(A\) and \(B\). Via techniques from \(L^p\)-harmonic analysis, perturbation theory and local spectral theory, it is shown that \(T\) satisfies certain local resolvent estimates, which imply the existence of local functional calculi and decomposability properties of \(T\).