Analytic approximation of matrix functions and dual extremal functions

Peller, V.

doi:10.1090/S0002-9939-08-09623-8

Analytic approximation of matrix functions and dual extremal functions
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Proc. Amer. Math. Soc. 137 (2009), 205-210 Request permission

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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