Methods of geometric function theory in classical and modern problems for polynomials

V. N. Dubinin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 4, pp. 599-684

Résumé

This paper gives a survey of classical and modern theorems on polynomials, proved using methods of geometric function theory. Most of the paper is devoted to results of the author and his students, established by applying majorization principles for holomorphic functions, the theory of univalent functions, the theory of capacities, and symmetrization. Auxiliary results and the proofs of some of the theorems are presented. Bibliography: 124 titles.

Détail

Keywords: majorization principles, Schwarz's lemma, capacities, univalent functions, symmetrization, inequalities, polynomials, critical points, critical values, rational functions.

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