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Optimal Recovery and n-Widths for Convex Classes of Functions

✍ Scribed by E. Novak


Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
656 KB
Volume
80
Category
Article
ISSN
0021-9045

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In this paper we find some exact values of \(n\)-widths in the integral metric with the Chebyshev weight function for the classes of functions that are bounded and analytic or harmonic in the interior of the ellipse with foci \(\pm 1\) and sum of semiaxes \(c\). We also construct optimal quadrature

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Let z be an analytic function with positive real part on ⌬ s z; z -1 with Ž . Ž . 0 s 1, Ј 0 ) 0 which maps the unit disk ⌬ onto a region starlike with respect Ž . to 1 and symmetric with respect to the real axis. Let ST denote the class of Ž . Ž . Ž . Ž . Ž . Ž . analytic functions f z with f 0 s