@article{a7394b0d701e4f91bfd9867cf6cb5863,

title = "Exact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function",

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.",

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",

author = "Adukov, {Victor M.} and Gennady Mishuris and Rogosin, {Sergei V.}",

note = "Funding Information: Funding. G.M. received a Royal Society Wolfson Research Merit Award. V.M.A. was supported by South Ural State University, Act 211 Government of the Russian Federation, contract no. 02.A03.21.0011. Acknowledgements. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for the Simon Fellowship and for all support and hospitality during the WHT programme {\textquoteleft}Bringing pure and applied analysis together via the Wiener–Hopf technique, its generalizations and applications{\textquoteright}, where work on this paper was undertaken. This programme was supported by EPSRC grant no. EP/R014604/1. The authors are grateful to Professor Ilya Spitkovsky for fruitful discussions on the results of the paper. Publisher Copyright: {\textcopyright} 2020 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.",

year = "2020",

month = may,

day = "27",

doi = "10.1098/rspa.2020.0099",

language = "English",

volume = "476",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "1364-5021",

publisher = "Royal Society",

number = "2237",

}