Norm estimates for function Lyapunov equations and applications

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We consider the function Lyapunov equation f*(A)X+Xf(A)=C, where A and C are given matrices, f(z) is a function holomorphic on a neighborhood of the spectrum σ(A) of A. For a solution X of that equation, norm estimates are established. By these estimates we investigate perturbations of a matrix A whose spectrum satisfies the condition infℜσ(f(A))>0. In the case f(z)=zν with a positive integer ν we obtain conditions that provide localization of the spectrum of a perturbed matrix in a given angle.

Original languageEnglish
Pages (from-to)4241-4247
Number of pages7
JournalJournal of the Franklin Institute
Issue number10
StatePublished - 1 Jul 2018


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