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 anlytic 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.
Readership: Professional and academic mathematicians of complex analysis, approximation theory and theoretical numerical analysis, graduate students in mathematics. Engineers, statisticians and theoretical physicists.
Qazi Ibadur Rahman, Department of Mathematics and Statistics, University of Montreal, Canada, and Gerhard Schmeisser, Mathematisches Institut, University of Erlangen-Nuremberg, Germany
"Presents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications ... Brings to the subject an immense range of reference to the study of polynomials. Professional and academic mathematicians of complex analysis, approximation theory and theoretical numerical analysis; graduate students in mathematics; engineers, statisticians and theoretical physicists, who have an interest in the important results about polynomials, will not do better than start with reading and referring to this book." - Current Engineering Practice
"A nicely written book that will be useful for scientists, engineers and mathematicians from other fields. It can be strongly recommended as an undergraduate or graduate text and as a comprehensive source for self study." - EMS
1: Introduction I Critical Points in Term of Zeros2: 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 Coefficients8: 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 Properties12: Growth estimates 13: Mean values 14: Derivative estimates on the unit disc 15: Derivative estimates on the unit interval 16: Coefficient estimates Bibliography Index
