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Monge-Ampère measures for convex bodies and Bernstein-Markov type inequalities

Burns, D. and Levenberg, N. and Mau, Sione N.P. and Révész, Sz. (2010) Monge-Ampère measures for convex bodies and Bernstein-Markov type inequalities. Transactions of the American Mathematical Society, 362 (12). pp. 6325-6340. ISSN 0002-9947

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We use geometric methods to calculate a formula for the complex Monge-Ampère measure, for a convex body and its Siciak-Zaharjuta extremal function. Bedford and Taylor had computed this for symmetric convex bodies. We apply this to show that two methods for deriving Bernstein-Markov type inequalities, i.e., pointwise estimates of gradients of polynomials, yield the same results for all convex bodies. A key role is played by the geometric result that the extremal inscribed ellipses appearing in approximation theory are the maximal area ellipses determining the complex Monge-Ampère solution Vk.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User: Ms Mereoni Camailakeba
Date Deposited: 27 May 2010 02:58
Last Modified: 25 Jul 2012 23:41

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