Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

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.

• Introduction.- Statement of Main Results.- Potential Theoretic Estimates.- Restricted Range Inequalities.- Bounds for Christoffel Functions.- Spacing of Zeros.- Bounds on Orthogonal Polynomials.- Markov-Bernstein Inequalities in L.- Discretization of Potentials.- Derivatives of Discretized Polynomials.- Weighted Polynomial Approximations.- Formulae Involving Bernstain-Szego Polynomials.- Asymptotics of Orthonormal Polynomials.- Further Bounds.- Universality Limits and 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)​