Agnieszka Kowalska
Polynomial approximation on semialgebraic sets
The Markov and Bernstein inequality estimated derivatives of polynomials in terms of their degrees and values on an interval or a circle. These inequalities play an important role in the constructive theory of functions. Many its generalization are still the subject of investigations. In particular, are known generalization of these inequalities for some compact subset of $\mathbb R^n$ or $\mathbb C^n$ and some curves. It is known that for $\mathbb C$ determining sets Markov's property is equivalent to some very interesting conditions. Some generalizations of Markov inequality on some semialgebraic sets will be presented.