Analytic theory of polynomials

Qazi Ibadur Rahman, G Schmeisser

756 pages, parution le 17/09/2002

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Résumé

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.

Contents

1-Critical points in terms of zeros

Fundamental results on critical points
More sophisticated method
More specific results on critical points
Applications to compositions of polynomials
Polynomials with real zeros
Conjectures and solutions

2-Zeros in terms of coefficients

Inclusion of all zeros
Inclusion of some of the zeros
Number of zeros in an interval
Number of zeros in a domain

3-Extremal properties

Growth estimates
Mean values
Derivative estimates on the unit disc
Derivative estimates on the unit interval
Coefficient estimates

Caractéristiques techniques

	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Qazi Ibadur Rahman, G Schmeisser
Parution	17/09/2002
Nb. de pages	756
Format	16 x 24
Couverture	Relié
Poids	1160g
Intérieur	Noir et Blanc
EAN13	9780198534938
ISBN13	978-0-19-853493-8