论文标题
关于C. Michel关于通常真实多项式模量的假设
On C. Michel's hypothesis about the modulus of typically real polynomials
论文作者
论文摘要
通常真实多项式的极端问题可以追溯到W. W. Rogosinski和G.szegő的纸，其中提出了许多问题，这些问题通过使用正交多项式来部分解决。从那时起，没有太多关于通常真实多项式的极端特性的新结果。朝这个方向的基本工作归功于M.〜Brandt，后者找到了一种解决极端问题的新方法。特别是，他解决了米歇尔（C. Michel）估计典型奇数多项式模量的问题。另一方面，D。K. Dimitrov展示了Fejér解决Rogosinski-Szegő问题的有效性。在本文中，我们通过使用Fejér的方法完全解决了米歇尔的问题。
Extremal problems for typically real polynomials go back to a paper by W. W. Rogosinski and G. Szegő, where a number of problems were posed, which were partially solved by using orthogonal polynomials. Since then, not too many new results on extremal properties of typically real polynomials have been obtained. Fundamental work in this direction is due to M.~Brandt, who found a novel way of solving extremal problems. In particular, he solved C. Michel's problem of estimating the modulus of a typically real polynomial of odd degree. On the other hand, D. K. Dimitrov showed the effectivity of Fejér's method for solving the Rogosinski--Szegő problems. In this article, we completely solve Michel's problem by using Fejér's method.
