Ukrainian Mathematical Bulletin

Volume 3, Issue 3, 2006 pp. 301-315.

Hadamard Inequality and Best Approximation of Functions in the Unit Disk

Authors: Mikhail Z. Dvejrin
Author institution: Donetsk National University, ul. Universitetskaya, 24, 83055, Donetsk Ukraine, Dvejrin@tcc-online.com, strannik35@telenet.dn.ua

Summary: We consider linear normed spaces of functions defined on the unit disk, with the norm that is invariant with respect to rotation of the argument. For such spaces, under natural conditions on the functions under consideration, we obtain a generalization of the Hadamard theorem on three circles, Bernstein inequalities, and some inequalities for best approximation with exact values of constants.

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