Analytic Theory of Polynomials: Critical Points, Zeros and Extremal Properties

by Qazi Ibadur Rahman, Gerhard Schmeisser

Overview

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.

Product Details

ISBN-13:	9780198534938
Publisher:	Oxford University Press
Publication date:	11/07/2002
Series:	London Mathematical Society Monographs , #26
Pages:	756
Product dimensions:	6.10(w) x 9.30(h) x 1.80(d)

About the Author

University of Montreal

Mathematisches Institut, University of Erlangen-Nuremberg

Table of Contents

1. IntroductionI. Critical Points in Term of Zeros2. Fundamental results on critical points3. More sophisticated methods4. More specific results on critical points5. Applications to compositions of polynomials6. Polynomials with real zeros7. Conjectures and solutionsII. Zeros in Terms of Coefficients8. Inclusion of all zeros9. Inclusion of some of the zeros10. Number of zeros in an interval11. Number of zeros in a domainIII. Extremal Properties12. Growth estimates13. Mean values14. Derivative estimates on the unit disc15. Derivative estimates on the unit interval16. Coefficient estimatesReferencesList of notationIndex

Editorial Reviews

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

From the Publisher