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# Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

- 1st Edition - February 10, 2022
- Authors: Robert B. Gardner, Narendra K. Govil, Gradimir V. Milovanović
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 1 9 8 8 - 4
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 2 0 0 7 - 1

Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they pl… Read more

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Request a sales quoteInequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only *Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials*, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.

- Applies Markov-Bernstein-type inequalities to any problem where derivative estimates are necessary
- Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions, and entire functions of exponential type
- Contains exhaustive references with more than five hundred citations to articles and books
- Features methods to solve inverse problems across approximation theory
- Includes open problems for further research

Graduate and PhD students working in mathematical analysis and approximation theory, especially in geometry of polynomials and complex approximation

- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- About the authors
- Preface
- Chapter 1: History and introduction: classical Markov–Bernstein inequalities
- Abstract
- 1.1. Markov's theorem and some of its generalizations and refinements
- 1.2. Markov–Duffin–Schaeffer inequalities and generalizations
- 1.3. Bernstein's inequality and some of its generalizations and refinements
- 1.4. Bernstein inequalities on several intervals and Szegő variants
- Bibliography
- Chapter 2: Different types of Bernstein inequalities
- Abstract
- 2.1. Bernstein-type inequalities concerning growth of polynomials
- 2.2. Bernstein-type inequalities for rational functions
- 2.3. Bernstein-type inequalities in the Lr norm
- 2.4. Bernstein-type inequalities in other environments
- 2.5. Bernstein-type inequalities for entire functions of exponential type
- Bibliography
- Chapter 3: Extremal problems of Markov–Bernstein type in integral norms
- Abstract
- 3.1. Orthogonal polynomials and classical weight functions
- 3.2. Extremal problems of Markov type in L2 norm for the classical weights
- 3.3. Different modifications of weighted L2 Markov–Bernstein's extremal problems and inequalities
- 3.4. Extremal problems of Markov type in Lr norm
- 3.5. Extremal problems of Markov type on the restricted classes of polynomials
- Bibliography
- Chapter 4: Bernstein-type inequalities for polynomials with restricted zeros
- Abstract
- 4.1. Inequalities for polynomials with zeros outside of a disk
- 4.2. Inequalities for polynomials with zeros inside of a disk
- 4.3. Inequalities for self-inversive and self-reciprocal polynomials
- 4.4. Inequalities for some other classes of polynomials
- Bibliography
- Chapter 5: Bernstein-type inequalities in the Lr norm
- Abstract
- 5.1. Introduction
- 5.2. Bernstein's inequality in Lr
- 5.3. The case of r>0
- Bibliography
- Chapter 6: Bernstein-type inequalities for polar derivatives of polynomials
- Abstract
- 6.1. Introduction
- 6.2. Extensions of the classical theorems of Grace and Laguerre
- 6.3. Bounds on the uniform norm of polar derivative of a polynomial
- 6.4. Bounds on the integral mean values of the polar derivative of a polynomial
- Bibliography
- Bibliography
- Bibliography
- Author index
- Subject index

- No. of pages: 442
- Language: English
- Edition: 1
- Published: February 10, 2022
- Imprint: Elsevier
- Paperback ISBN: 9780128119884
- eBook ISBN: 9780128120071

RG

### Robert B. Gardner

NG

### Narendra K. Govil

GM

### Gradimir V. Milovanović

*Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials*on ScienceDirect