A note on the transfinite diameter of Bernstein sets

Authors: ÖZCAN YAZICI

Abstract: A compact set $K\subset \mathbb C^n$ is called Bernstein set if, for some constant $M>0$, the following inequality $$||D^{\alpha}P||_K\leq M^{|\alpha|}(\deg P)^{|\alpha|}||P ||_K $$ is satisfied for every multiindex $\alpha\in \mathbb N^n$ and for every polynomial $P$. We provide here a lower bound for the transfinite diameter of Bernstein sets by using generalized extremal Leja points.

Keywords: Transfinite diameter, Bernstein and Markov sets, Pluripolar sets, Leja points

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