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
Full text not available from this repository.Abstract
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 |
| URI: | https://repository.usp.ac.fj/id/eprint/1901 |
Actions (login required)
 |
View Item |