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Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities

Volume 141 / 2000

M. Baran, W. Pleśniak Studia Mathematica 141 (2000), 221-234 DOI: 10.4064/sm-141-3-221-234

Abstract

We show that in the class of compact sets K in $ℝ^n$ with an analytic parametrization of order m, the sets with Zariski dimension m are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for tangential derivatives of (the traces of) polynomials on K.

Authors

  • M. Baran
  • W. Pleśniak

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