Аннотация:
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.
