ON POLYNOMIALS WITH CONSTRAINTS ON CIRCULAR ARCS

摘要

It is shown that for polynomials with prescribed minimal and maximal values of their moduli on a union of circular arcs, new covering and distortion theorems, as well as estimates for the modulus of the product of the leading coefficient and constant term, follow from the majorization principle for meromorphic functions proved by the authors earlier. As corollaries, recent results on polynomials with additional constraints on their zeros established by other mathematicians are obtained. Bibliography: 16 titles.