Topics in Polynomials: Extremal Problems, Inequalities, Zeros

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The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.
 

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Contents

CHAPTER 1
1
polynomials
22
CHAPTER 2
85
CHAPTER 3
173
RELATED TOPICS
216
CHAPTER 4
299
CHAPTER 5
383
WEIGHTED POLYNOMIAL INEQUALITIES
471
CHAPTER 6
527
in RN
560
CHAPTER 7
725
GEOMETRIC DESIGN
757
Symbol Index
783
Subject Index
803
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Page 711 - RI 02904, but References should be styled and punctuated according to the following examples: 1 . GG Lorentz, The degree of approximation by polynomials with positive coefficients, Math. Ann. 151 (1963), 239-251.

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