Аннотация:
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 pT 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 + az1+T + bz1+2T
.
Also, there are suggested hypotheses for the general case in the
work
