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- W2039449660 abstract "We 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 $Phi$ and the notion of a canonical factorization of a very badly approximable matrix function $Phi$. 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 $Phi$ 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 $Phiin X$ implies that all factors in a canonical factorization of $Phi$ belong to the same space $X$. In the last section we characterize the very badly approximable unitary-valued functions $U$ that satisfy the condition $|H_U|_{text e}<1$." @default.
- W2039449660 created "2016-06-24" @default.
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- W2039449660 date "2001-01-26" @default.
- W2039449660 modified "2023-09-27" @default.
- W2039449660 title "Badly approximable matrix functions and canonical factorizations" @default.
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