Matrix functions nonregular on the convex hull of the spectrum

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Abstract

In this article, matrix-valued functions nonregular on the convex hull of the spectrum are considered. The logarithm, root and meromorphic functions of various matrices are examples of such functions. Here sharp norm estimates are established for the considered matrix-valued functions. Applications of the obtained estimates to the periodic problem and two-points boundary value problem for vector differential equations are also discussed.

Original languageEnglish
Pages (from-to)465-473
Number of pages9
JournalLinear and Multilinear Algebra
Volume60
Issue number4
DOIs
StatePublished - 1 Apr 2012

Keywords

  • matrix-valued functions
  • nonregular matrix functions
  • periodic problem
  • two-points boundary value problem
  • vector differential equations

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