Analytic Theory of Polynomials Critical Points, Zeros and Extremal Properties [Hardcover]

This text presents easy to understand proofs of some of the most difficult results about polynomials. It encompasses a self-contained account of the properties of polynomials as analytic functions of a special kind.
The zeros of compositions of polynomials are also investigated along with their growth, and some of these considerations lead to the study of analogous questions for trigonometric polynomials and certain transcendental entire functions. The strength of methods are fully explained and demonstrated by means of applications.

1. Introduction
I. Critical Points in Term 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
References
List of notation
Index

This book ought to find its place in every mathematical library and will become a basic source for references. --Mathematical Reviews