Unitary interpolants and factorization indices of matrix functions
| dc.creator | Alexeev, R. B. | |
| dc.creator | Peller, V. V. | |
| dc.date | 2001-01-26 | |
| dc.date.accessioned | 2026-07-07T04:39:50Z | |
| dc.date.available | 2026-07-07T04:39:50Z | |
| dc.description | For an $n\times n$ bounded matrix function $Φ$ we study unitary interpolants $U$, i.e., unitary-valued functions $U$ such that $\hat U(j)=\hatΦ(j)$, $j<0$. We are looking for unitary interpolants $U$ for which the Toeplitz operator $T_U$ is Fredholm. We give a new approach based on superoptimal singular values and thematic factorizations. We describe Wiener--Hopf factorization indices of $U$ in terms of superoptimal singular values of $Φ$ and thematic indices of $Φ-F$, where $F$ is a superoptimal approximation of $Φ$ by bounded analytic matrix functions. The approach essentially relies on the notion of a monotone thematic factorization introduced in [AP]. In the last section we discuss hereditary properties of unitary interpolants. In particular, for matrix functions $Φ$ of class $H^\be+C$ we study unitary interpolants $U$ of class $QC$. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0101224 | |
| dc.identifier | http://arxiv.org/abs/math/0101224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60830 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 47B35, 46E15, 30D55 | |
| dc.title | Unitary interpolants and factorization indices of matrix functions | |
| dc.type | text |