Characterization of Jordan Vectors of Operator-Valued Functions with Applications in Differential Equations

Abstract

A well-known characterization of Jordan vectors of a matrix polynomial $L(z)$ is generalized to a characterization of Jordan vectors of the operator-valued function $Q(z)$ at an eigenvalue $\alpha \in \mathbb{C}$. The results are then applied to solve a system of nonlinear ordinary differential equations.

arXiv commentAccepted for publication in "Sarajevo Journal of Mathematics". 12 pages