论文标题
折叠对称性三项官方的极端问题
Extremal problems for trinomials with fold symmetry
论文作者
论文摘要
著名的T. dysridge多项式具有许多极端特性：当领先系数最大时，系数的最大性；衍生物的零位于单位圆上；用schlicht归一化拉伸单位磁盘的最大半径$ f（0）= 0 $，$ f'（0）= 1 $;单位磁盘收缩的最大尺寸沿真实轴的方向，即归一化$ f（0）= 0 $，$ f（1）= 1。但是，在标准的对称方法下，$ \ sqrt [t] {t] {f（z^t）} $，这些polynomials to to to to dolynomials domynomials，不是多元型的。我们如何使用具有类似于Companridge多项式的特性的折叠对称性构造多项式？相应的极端问题在上述极端问题中会有什么值？该论文致力于解决这些问题的the Trinomials $ f（z）= z+az^{1+t}+bz^{1+2t} $。此外，还建议对工作中的一般情况进行建议。
The famous T. Suffridge polynomials have many extremal properties: the maximality of coefficients when the leading coefficient is maximal; the zeros of the derivative are located on the unit circle; the maximum radius of stretching the unit disk with the schlicht normalization $F(0)=0$, $F'(0)=1$; the maximum size of the unit disk contraction in the direction of the real axis for univalent polynomials with the normalization $F(0)=0$, $F(1)=1.$ However, under the standard symmetrization method $\sqrt[T]{F(z^T)}$, these polynomials go to functions, which are not polynomials. How can we construct the polynomials with fold symmetry that have properties similar to those of the Suffridge polynomial? What values will the corresponding extremal quantities take in the above-mentioned extremal problems? The paper is devoted to solving these questions for the case of the trinomials $F(z)=z+az^{1+T}+bz^{1+2T}$. Also, there are suggested hypotheses for the general case in the work.
