Superoptimal analytic approximations of matrix functions.

Peller, V. V. and Young, N. J. (1994) Superoptimal analytic approximations of matrix functions. Journal of Functional Analysis, 120 (2). pp. 300-343.

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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).

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Journal Article
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Journal of Functional Analysis
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12 Nov 2008 15:10
Last Modified:
21 Nov 2022 18:34