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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Analytic approximation of matrix functions and dual extremal functions


Author: V. V. Peller
Journal: Proc. Amer. Math. Soc. 137 (2009), 205-210
MSC (2000): Primary 47B35, 46E40, 30D55, 30E10
Published electronically: August 4, 2008
MathSciNet review: 2439442
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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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Additional Information

V. V. Peller
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09623-8
PII: S 0002-9939(08)09623-8
Keywords: Best approximation, badly approximable matrix functions, dual extremal function, Hankel operator, maximizing vector
Received by editor(s): December 18, 2007
Published electronically: August 4, 2008
Additional Notes: The author is partially supported by NSF grant DMS 0700995
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.