Regular approximate factorization of a class of matrix-function with an unstable set of partial indices

Gennady Mishuris, Sergei Rogosin

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

15 Dyfyniadau(SciVal)
135 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

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 nonsingular 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
Iaith wreiddiolSaesneg
Rhif yr erthygl0170279
CyfnodolynProceedings of the Royal Society of Edinburgh, Section A: Mathematics
Cyfrol474
Rhif cyhoeddi2209
Dyddiad ar-lein cynnar17 Ion 2018
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 31 Ion 2018

Ôl bys

Gweld gwybodaeth am bynciau ymchwil 'Regular approximate factorization of a class of matrix-function with an unstable set of partial indices'. Gyda’i gilydd, maen nhw’n ffurfio ôl bys unigryw.

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