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On Location of the Matrix Spectrum with Respect to a Parabola
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Journal Article
On Location of the Matrix Spectrum with Respect to a Parabola
2023
Overview
In the present article, we consider the problem on location of the matrix spectrum with respect to a parabola. In terms of solvability of a matrix Lyapunov type equation, we prove theorems on location of the matrix spectrum in certain domains
(bounded by a parabola) and
(lying outside the closure of
). A solution to the matrix equation is constructed. We use this equation and prove an analog of the Lyapunov–Krein theorem on dichotomy of the matrix spectrum with respect to a parabola.
Publisher
Pleiades Publishing,Springer Nature B.V
Subject
