Polynomials and Polynomial Inequalities, Springer-Verlag

polynomials and polynomial inequalities,

Polynomials and Polynomial Inequalities,
by Peter Borwein & Tamas Erdelyi

Graduate Texts in Mathematics # 161,
Springer-Verlag, New York, 1995
ISBN 0-387-94509-1

Table of Contents

CHAPTER 1 Introduction and Basic Properties 1

1.1 Polynomials and Rational Functions
1.2 The Fundamental Theorem of Algebra
1.3 Zeros of the Derivative

CHAPTER 2 Some Special Polynomials 29

2.1 Chebyshev Polynomials
2.2 Orthogonal Functions
2.3 Orthogonal Polynomials
2.4 Polynomials with Nonnegative Coefficients

CHAPTER 3 Chebyshev and Descartes Systems 91

3.1 Chebyshev Systems
3.2 Descartes Systems
3.3 Chebyshev Polynomials in Chebyshev Spaces
3.4 Muntz Polynomials
3.5 Chebyshev Polynomials in Rational Spaces

CHAPTER 4 Denseness Questions 154

4.1 Variations on the Weierstrass Theorem
4.2 Muntz's Theorem
4.3 Unbounded Bernstein Inequalities
4.4 Muntz Rationals

CHAPTER 5 Basic Inequalities 227

5.1 Classical Polynomial Inequalities
5.2 Markov's Inequality for Higher Derivatives
5.3 Inequalities for Norms of Factors

CHAPTER 6 Inequalities in Muntz Spaces 275

6.1 Inequalities in Muntz Spaces
6.2 Nondense Muntz Spaces

CHAPTER 7 Inequalities for Rational Function Spaces 320

7.1 Inequalities for Rational Function Spaces
7.2 Inequalities for Logarithmic Derivatives

APPENDIX A1 Algorithms and Computational Concerns 356
APPENDIX A2 Orthogonality and Irrationality 372
APPENDIX A3 An Interpolation Theorem 382
APPENDIX A4 Inequalities for Generalized Polynomials in L_p 392
APPENDIX A5 Inequalities for Polynomials with Constraints 417
BIBLIOGRAPHY 448
NOTATION 467
INDEX 473