Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$

A. L. Levin · Doron Shaul Lubinsky

Jan. 1994 · American Mathematical Society: Memoirs of the American Mathematical Society Buch 535 · American Mathematical Soc.

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Bounds for orthogonal polynomials which hold on the whole interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on $[-1,1]$. Levin and Lubinsky obtain such bounds for weights that vanish strongly at 1 and $-1$. They also present uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.