复平面上关于有理Bernstein-Markov性质的一些结果
Some results on the rational Bernstein Markov property in the complex plane
AI总结：
本文研究有理函数的Bernstein-Markov性质变体，比较多项式与有理函数的条件，提出充分条件及质量密度条件。
摘要：
Bernstein Markov性质（BMP）是对紧集上多项式或有理函数的统一范数增长的渐进行量假设，其中μ为正有限测度。本文考虑两种有理函数的BMP变体，比较其与多项式BMP的关系，发现后者能推出前者的一些充分条件。此外，本文恢复了测量其支持集上满足有理BMP的充分质量密度条件。
英文摘要：
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 μ 2 -norms, where μ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
