Power bounded and exponentially bounded matrices.
The authors prove spectral decompositions for the power and exponentially bounded matrices and apply these results to obtain series and integral representations of the Drazin inverse and to describe the asymptotic behaviour of solutions of linear ordinary differential equations, including the singular and singularly perturbed ones. An example of localized travelling waves for a system of conservation laws is given. In the proofs a new characterization of eigenprojections obtained in the paper is utilized.
power and exponentially bounded matrices
singularly perturbed differential equations
scientific article; zbMATH DE number 2165524