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Analytic theory of polynomials

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Author(s): Schmeisser, Gerhard; Rahman, Qazi Ibadur
Series: London Mathematical Society monographs new series no. 26
Publisher: Clarendon Press, Oxford University Press
Year: 2002

Language: English
Pages: 742
City: New York, Oxford
Tags: Polynomials.;Analytic functions.;Polynômes.;Fonctions analytiques.;Analytische functies.;Nullstelle.;Singularität ;Geometrische Funktionentheorie.;Polynom.

Content: 1. Introduction --
I. Critical Points in Terms of Zeros. 2. Fundamental results on critical points. 3. More sophisticated methods. 4. More specific results on critical points. 5. Applications to compositions of polynomials. 6. Polynomials with real zeros. 7. Conjectures and solutions --
II. Zeros in Terms of Coefficients. 8. Inclusion of all zeros. 9. Inclusion of some of the zeros. 10. Number of zeros in an interval. 11. Number of zeros in a domain --
III. Extremal Properties. 12. Growth estimates. 13. Mean values. 14. Derivative estimates on the unit disc. 15. Derivative estimates on the unit interval. 16. Coefficient estimates.