Power bounded and exponentially bounded matrices. (English) Zbl 1060.34506

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.


34D05 Asymptotic properties of solutions to ordinary differential equations
15A09 Theory of matrix inversion and generalized inverses
34E15 Singular perturbations for ordinary differential equations
39A11 Stability of difference equations (MSC2000)
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