Orthogonal Polynomials for Exponential Weights (CMS Books in Mathematics)

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Orthogonal Polynomials for Exponential Weights - Eli Levin, Doron S. Lubinsky - Google Книги

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Orthogonal properties of Legendre (MATH)

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Volume 10 (2012)

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Jail calls is here to help you. If you have an issue with service, one of our friendly customer service representatives will gladly answer your questions. It continues an investigation initiated and developed in a sequence of prior works whose ultimate aim is to reveal and understand, in a rigorous way, the deep connections between correlation functions for eigenvalues of these random matrix ensembles on the one hand and the enumerative interpretations of their matrix moments in terms of map combinatorics a branch of graph theory on the other.

In doing this we make essential use of the link between the asymptotics of the random matrix partition function and orthogonal polynomials with exponential weight equal to the random matrix potential.


Along the way we develop and analyze the continuum limits of both the Toda lattice equations and the difference string equations associated to these orthogonal polynomials. The former are found to have the structure of a hierarchy of near-conservation laws; the latter are a novel semi-classical extension of the traditional string equations. 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. Recensie s From the reviews: It cannot serve as a textbook but will probably be indispensable for research in this field, since all the important tools, results, and properties are there, with detailed proofs and appropriate references.

This book is the result of almost 2 decades of collaboration of the two authors. The style is a succession of theorems and proofs, clearly written, introducing the necessary definitions and concepts where needed. A must for researchers in orthogonal polynomials or in approximation theory, or in any other field where orthogonal polynomials play an essential role.

With its attention to new results It will undoubtedly be of considerable use to researchers in this area There is no doubt that this book is a substantial contribution to the literature on orthogonal polynomials