The analysis of orthogonal polynomials associated with general weights has been a major theme in classical analysis this century. In this monograph, the authors define and discuss their classes of weights, state several of their results on Christoffel functions, Bernstein inequalities, restricted range inequalities, and record their bounds on the orthogonal polynomials, as well as their asymptotic results. This book will be of interest to researchers in approximation theory, potential theory, as well as in some branches of engineering.

Introduction and Results Weighted Potential Theory: The Basics Basic Estimates for Q, a_t Restricted Range Inequalities Estimates for Measure and Potential Smoothness of /rho_t Weighted Polynomial Approximation Asymptotics of Extremal Errors Christoffel Functions Markov-Bernstein and Nikolskii Inequalities Zeros of Orthogonal Polynomials Bounds on Orthogonal Polynomials Further Bounds and Applications Asymptotics of Extremal Polynomials Asymptotics of Orthonormal Polynomials

Eli (A.L.) Levin received the Ph.D degree in Mathematics from Moscow State University in 1970. In 1979 he joined the Faculty of the Open University of Israel in Tel Aviv, where he is currently Associate Professor.

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