Some results on the rational Bernstein Markov property in the complex plane

Federico Piazzon

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arXiv · 1502.03256

Some results on the rational Bernstein Markov property in the complex plane

Federico Piazzon

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Abstract

The Bernstein Markov Property, shortly BMP, is an asymptotic quan- titative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to L {\mu} 2 -norms, where {\mu} is a positive finite measure. We consider two variants of BMP for rational functions with restricted poles and compare them with the polynomial BMP finding out some sufficient condi- tions for the latter to imply the former. Moreover, we recover a sufficient mass- density condition for a measure to satisfy the rational BMP on its support.

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Federico Piazzon. 2015-02-11. Some results on the rational Bernstein Markov property in the complex plane. https://arxiv.org/abs/1502.03256

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