Affiliation:
1. Department of Mathematics, Aberystwyth University, Penglais, SY23 3BZ Aberystwyth, UK
2. Department of Economics, Belarusian State University, Nezavisimosti Avenue, 4, 220030 Minsk, Belarus
Abstract
From the classic work of Gohberg & Krein (1958
Uspekhi Mat. Nauk.
XIII
, 3–72. (Russian).), it is well known that the set of partial indices of a non-singular matrix function may change depending on the properties of the original matrix. More precisely, it was shown that if the difference between the largest and the smallest partial indices is larger than unity then, in any neighbourhood of the original matrix function, there exists another matrix function possessing a different set of partial indices. As a result, the factorization of matrix functions, being an extremely difficult process itself even in the case of the canonical factorization, remains unresolvable or even questionable in the case of a non-stable set of partial indices. Such a situation, in turn, has became an unavoidable obstacle to the application of the factorization technique. This paper sets out to answer a less ambitious question than that of effective factorizing matrix functions with non-stable sets of partial indices, and instead focuses on determining the conditions which, when having known factorization of the limiting matrix function, allow to construct another family of matrix functions with the same origin that preserves the non-stable partial indices and is close to the original set of the matrix functions.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献