Bernstein Type Theorems for Compact Sets in Rn Revisited

✍ Scribed by M. Baran

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 266 KB
• Volume: 79
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1994.1124

✦ Synopsis

In this paper we complete some results of (J. Approx. Theory 69 (1992), 156-166) and give a geometrical approach to the multivariate Bernstein and Markov inequalities. The most interesting and slightly surprising result is a sharp Markov inequality for convex symmetric subsets of (\mathbf{R}^{n}) formulated in geometrical language. A sharp inequality for gradients of polynomials extends an old Kellog result (Math. Z. 27 (1927), 55-64), and it is also a partial positive answer to a question formulated by Wilhelmsen (J. Approx. Theory 11 (1974), 216-220) in 1974. (C) 1994

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