Exact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function

Victor M. Adukov*, Gennady Mishuris, Sergei V. Rogosin

*Corresponding author for this work

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Abstract

The possible instability of partial indices is one of the important constraints in the creation of approximate methods for the factorization of matrix functions. This paper is devoted to a study of a specific class of triangular matrix functions given on the unit circle with a stable and unstable set of partial indices. Exact conditions are derived that guarantee a preservation of the unstable set of partial indices during a perturbation of a matrix within the class. Thus, even in this probably simplest of cases, when the factorization technique is well developed, the structure of the parametric space (guiding the types of matrix perturbations) is non-trivial.

Original languageEnglish
Article number20200099
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume476
Issue number2237
DOIs
Publication statusPublished - 27 May 2020

Keywords

  • Essential polynomials
  • Factorization of matrix functions
  • Toeplitz matrix
  • Triangular matrices
  • Wiener algebra
  • essential polynomials
  • Special feature
  • triangular matrices
  • factorization of matrix functions
  • Research articles

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