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Author: Eli Levin Publisher: Springer ISBN: 3319729470 Category : Mathematics Languages : en Pages : 170
Book Description
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.
Author: Eli Levin Publisher: Springer ISBN: 3319729470 Category : Mathematics Languages : en Pages : 170
Book Description
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.
Author: Eli Levin Publisher: Springer Science & Business Media ISBN: 1461302013 Category : Mathematics Languages : en Pages : 472
Book Description
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.
Author: Nicholas J. Daras Publisher: Springer Nature ISBN: 3031464877 Category : Mathematics Languages : en Pages : 474
Book Description
This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Author: Gabor Szeg Publisher: American Mathematical Soc. ISBN: 0821810235 Category : Mathematics Languages : en Pages : 432
Book Description
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
Author: Doron S. Lubinsky Publisher: Springer ISBN: 3540388575 Category : Mathematics Languages : en Pages : 160
Book Description
0. The results are consequences of a strengthened form of the following assertion: Given 0 p, f Lp ( ) and a certain sequence of positive numbers associated with Q(x), there exist polynomials Pn of degree at most n, n = 1,2,3..., such that if and only if f(x) = 0 for a.e.
Author: Francesco Aldo Costabile Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110757249 Category : Mathematics Languages : en Pages : 526
Book Description
Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.
Author: A. L. Levin Publisher: American Mathematical Soc. ISBN: 9780821862582 Category : Mathematics Languages : en Pages : 162
Book Description
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.
Author: Vilmos Totik Publisher: Springer ISBN: 3540483233 Category : Mathematics Languages : en Pages : 119
Book Description
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Author: Eli Levin
Author: Eli Levin
Author: Eli Levin
Author: Nicholas J. Daras
Author: Gabor Szeg
Author: Doron S. Lubinsky
Author: Francesco Aldo Costabile![Christoffel Functions and Orthogonal Polynomials for Exponential Weights on [-1,1] PDF](https://books.google.com/books/content/images/frontcover/bKCi5w9dj4QC?fife=w80-h100)
Author: A. L. Levin
Author: Vilmos Totik
Author: J. Baik
Author: Herbert Stahl