Abstract
Condition spectrum is an essential generalization of the spectrum. This article considers the condition spectrum of bounded linear operators on Banach space and develops certain topological properties. It is observed that the condition spectrum is useful than the spectrum and pseudospectrum for identifying the norm behavior of non-normal matrices. For a bounded linear operator A on a Banach space, we find upper and lower bounds for \(\Vert e^{tA}\Vert , \, t\ge 0\) and \(\Vert A^n\Vert ,\, n=1,2,\ldots\) using the condition spectrum of A. These bounds are used to identify the transient effect of the quantities appearing in the time dependent linear dynamical system.
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The author would like to thank the referee for the valuable comments. The SERB MATRICS grant supported this author’s work with project reference no. MTR/2021/000028.
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Kumar, G.K. Determination of Transient Effect in Time-Dependent Linear Dynamical System Using Condition Spectrum. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00623-w
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DOI: https://doi.org/10.1007/s12591-022-00623-w
Keywords
- Spectrum
- Resolvent norm
- Pseudospectrum
- Condition spectrum
- Time dependent linear dynamical system
- Transient effect