Analytic approximation of matrix functions and dual extremal functions

2007/11/18 by V. V. Peller, Vladimir Peller, Peller, V. V.
Mathematics · #30E10 #47B35 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical functions and polynomials #Spectral Theory (math.SP) #math.CA #math.CV #math.FA #math.SP #msc:30E10 #msc:47B35

paper · pdf · doi:10.48550/arxiv.0711.2771

openalex publication_date 2007/11/18 · arxiv created 2008/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain special factorizations that involve thematic matrix functions.

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