Badly approximable matrix functions and canonical factorizations

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dc.creatorAlexeev, R. B.
dc.creatorPeller, V. V.
dc.date2001-01-26
dc.date.accessioned2026-07-07T04:39:50Z
dc.date.available2026-07-07T04:39:50Z
dc.descriptionWe continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $Φ$ and the notion of a canonical factorization of a very badly approximable matrix function $Φ$. Such factorizations are defined in terms of so-called balanced unitary-valued functions which have many remarkable properties. Unlike the case of thematic factorizations studied earlier in [PY1], [PY2], [PT], [AP1], the factors in canonical factorizations (as well as partial canonical factorizations) are uniquely determined by the matrix function $Φ$ up to constant unitary factors. We study many properties of canonical factorizations. In particular we show that under certain natural assumptions on a function space $X$ the condition $Φ\in X$ implies that all factors in a canonical factorization of $Φ$ belong to the same space $X$. In the last section we characterize the very badly approximable unitary-valued functions $U$ that satisfy the condition $\|H_U\|_{\text e}<1$.
dc.description36 pages
dc.identifierhttps://arxiv.org/abs/math/0101225
dc.identifierhttp://arxiv.org/abs/math/0101225
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60831
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subject47B35, 46E15, 30D55
dc.titleBadly approximable matrix functions and canonical factorizations
dc.typetext

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