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Superoptimal analytic approximations of matrix functions.

Research output: Contribution to journalJournal articlepeer-review

Published
  • V. V. Peller
  • N. J. Young
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<mark>Journal publication date</mark>1994
<mark>Journal</mark>Journal of Functional Analysis
Issue number2
Volume120
Number of pages44
Pages (from-to)300-343
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We study the approximation of a bounded matrix-valued function G on the unit circle by functions Q bounded and analytic in the unit disc. We show that if G is continuous then there is a unique Q for which the error G - Q has a strong minimality property involving not only the L∞-norm of G - Q but also the suprema of its subsequent singular values. We obtain structural properties of the error G - Q and show that certain smoothness properties of G are inherited by Q (e.g., membership of Besov spaces).