2001/01/26 by R. B. Alexeev, V. V. Peller, Alexeev, R. B. +1
Computer Science · Mathematics · #30D55 #46E15 #47B35 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.CA #math.CV #math.FA #msc:30D55 #msc:46E15 #msc:47B35
paper · pdf · doi:10.48550/arxiv.math/0101224
20 pages
arxiv created 2001/01/26 · openalex publication_date 2001/01/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an n× n bounded matrix function Φ we study unitary interpolants U, i.e., unitary-valued functions U such that U(j)=Φ(j), j<0. We are looking for unitary interpolants U for which the Toeplitz operator TU 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.