Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

1. Front Matter

   Pages i-vii

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2. Introduction

   • Eli Levin, Doron S. Lubinsky

   Pages 1-8

3. Statement of Main Results

   • Eli Levin, Doron S. Lubinsky

   Pages 9-12

4. Potential Theoretic Estimates

   • Eli Levin, Doron S. Lubinsky

   Pages 13-27

5. Restricted Range Inequalities

   • Eli Levin, Doron S. Lubinsky

   Pages 29-35

6. Bounds for Christoffel Functions

   • Eli Levin, Doron S. Lubinsky

   Pages 37-45

7. Spacing of Zeros

   • Eli Levin, Doron S. Lubinsky

   Pages 47-51

8. Bounds on Orthogonal Polynomials

   • Eli Levin, Doron S. Lubinsky

   Pages 53-62

9. Markov-Bernstein Inequalities in L _∞

   • Eli Levin, Doron S. Lubinsky

   Pages 63-65

10. Discretization of Potentials

    • Eli Levin, Doron S. Lubinsky

    Pages 67-82

11. Derivatives of Discretized Polynomials

    • Eli Levin, Doron S. Lubinsky

    Pages 83-92

12. Weighted Polynomial Approximations

    • Eli Levin, Doron S. Lubinsky

    Pages 93-115

13. Formulae Involving Bernstein-Szegő Polynomials

    • Eli Levin, Doron S. Lubinsky

    Pages 117-122

14. Asymptotics of Orthonormal Polynomials

    • Eli Levin, Doron S. Lubinsky

    Pages 123-142

15. Further Bounds

    • Eli Levin, Doron S. Lubinsky

    Pages 143-151

16. Universality Limits and Entropy Integrals

    • Eli Levin, Doron S. Lubinsky

    Pages 153-164

17. Back Matter

    Pages 165-170

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This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.  Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. 

This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. 

• Orthogonal Polynomials
• Varying Weights
• Asymptotics
• Universality Limits
• Christoffel Functions
• Exponential Weights
• Asymptotics
• Christoffel Functions
• Entropy Integrals

“This book is written by two well-reputed specialists on orthogonal polynomials. Thus, It will be of great interest to those studying orthogonal polynomials, as well as Ph.D. students specializing in this or related areas. The structure of the text is nice. In fifteen short chapters the authors provide us with the statement of the results and their corresponding proofs in a rigorous and precise way.” (Juan José Monero-Balcázar, Mathematical Reviews, October, 2018)​

• Department of Mathematics, Open University of Israel, Tel-Aviv, Israel

  Eli Levin

• Mathematics, Georgia Institution of Technology, Atlanta, USA

  Doron S. Lubinsky

Eli Levin is an emeritus professor at the Open University of Israel in Ramat Aviv. 

Doron Lubinsky is a professor at Georgia Institute of Technology. Both are authors of papers on approximation theory, and a joint monograph on orthogonal polynomials.

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