Remarks on the perturbation of analytic matrix functions. II
type: Item
instance of: scholarly article
title: Remarks on the perturbation of analytic matrix functions. II
zbMATH Open document ID: 0682.47004
DOI: 10.1007/BF01235739
published in: Integral Equations and Operator Theory
publication date: 1989-01-01T00:00:00Z
review text: Let A(\(\lambda)\), B(\(\lambda\),\(\epsilon)\) be \(n\times n\) matrix functions, holomorphic near \(\lambda =\lambda_ 0\) and \(\epsilon =0\), \(B(\lambda,0)=0\), and let \(\lambda_ 0\) be an eigenvalue of A(\(\lambda)\) with partial multiplicities \(m_ 1,...,m_ g\). Using the Newton diagram, a sufficient condition is given which ensures that for each partial multiplicity \(m_ j\) there are \(m_ j\) eigenvalues \(\lambda_{j\sigma}(\epsilon)\) of \(T(\lambda,\epsilon)=A(\lambda)+B(\lambda,\epsilon)\) with an expansion \(\lambda_{j\sigma}(\epsilon)=\lambda_ 0+\alpha_{j\sigma}\epsilon^{1/m_ j}+o(| \epsilon |^{1/m_ j})\) for small \(\epsilon\), \(\alpha_{j\sigma}\neq 0\); \(\sigma =1,...,m_ j\), \(j=1,...,g\). This result is specialized to hermitian matrix functions and \(\lambda\)-linear problems. This note is a correction and extension of the earlier work by the second author: Integral Equations Oper. Theory 9, 592-599 (1986; Zbl 0605.47013).
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 15A22
zbMATH DE Number: 4117261
zbMATH Keywords: Newton diagram
zbMATH Keywords: partial multiplicity
zbMATH Keywords: hermitian matrix functions
author: Heinz Langer
author: B. Najman
MaRDI profile type: Publication
Wikidata QID: Q124629876
cites work: Q3675005
cites work: Remarks on the perturbation of analytic matrix functions
cites work: Eigenvalues of the Klein-Gordon equation
cites work: Q5683231
full work available at URL: https://doi.org/10.1007/bf01235739
OpenAlex ID: W4236327515
description: scientific article; zbMATH DE number 4117261