Bounds And Asymptotics For Orthogonal Polynomials For Varying Weights
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Bounds And Asymptotics For Orthogonal Polynomials For Varying Weights
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Author : Eli Levin
language : en
Publisher: Springer
Release Date : 2018-02-13
Bounds And Asymptotics For Orthogonal Polynomials For Varying Weights written by Eli Levin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.
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.
Exploring Mathematical Analysis Approximation Theory And Optimization
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Author : Nicholas J. Daras
language : en
Publisher: Springer Nature
Release Date : 2024-01-04
Exploring Mathematical Analysis Approximation Theory And Optimization written by Nicholas J. Daras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.
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.
Logarithmic Potentials With External Fields
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Author : Edward B. Saff
language : en
Publisher: Springer Nature
Release Date : 2024-10-04
Logarithmic Potentials With External Fields written by Edward B. Saff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-04 with Mathematics categories.
This is the second edition of an influential monograph on logarithmic potentials with external fields, incorporating some of the numerous advancements made since the initial publication. As the title implies, the book expands the classical theory of logarithmic potentials to encompass scenarios involving an external field. This external field manifests as a weight function in problems dealing with energy minimization and its associated equilibria. These weighted energies arise in diverse applications such as the study of electrostatics problems, orthogonal polynomials, approximation by polynomials and rational functions, as well as tools for analyzing the asymptotic behavior of eigenvalues for random matrices, all of which are explored in the book. The theory delves into diverse properties of the extremal measure and its logarithmic potentials, paving the way for various numerical methods. This new, updated edition has been thoroughly revised and is reorganized into three parts, Fundamentals, Applications and Generalizations, followed by the Appendices. Additions to the new edition include: new material on the following topics: analytic and C2 weights, differential and integral formulae for equilibrium measures, constrained energy problems, vector equilibrium problems, and a probabilistic approach to balayage and harmonic measures; a new chapter entitled Classical Logarithmic Potential Theory, which conveniently summarizes the main results for logarithmic potentials without external fields; several new proofs and sharpened forms of some main theorems; expanded bibliographic and historical notes with dozens of additional references. Aimed at researchers and students studying extremal problems and their applications, particularly those arising from minimizing specific integrals in the presence of an external field, this book assumes a firm grasp of fundamental real and complex analysis. It meticulously develops classical logarithmic potential theory alongside the more comprehensive weighted theory.
Polynomial Sequences
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Author : Francesco Aldo Costabile
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-12-18
Polynomial Sequences written by Francesco Aldo Costabile and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-18 with Mathematics categories.
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.
Orthogonal Polynomials For Exponential Weights
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Author : Eli Levin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Orthogonal Polynomials For Exponential Weights written by Eli Levin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century, and undoubtedly will continue to grow in importance in the future. In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0; likewise the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov- Bernstein and Nikolskii inequalities. The authors have collaborated actively since 1982 on various topics, and have published many joint papers, as well as a Memoir of the American Mathematical Society. The latter deals with a special case of the weights treated in this book. In many ways, this book is the culmination of 18 years of joint work on orthogonal polynomials, drawing inspiration from the works of many researchers in the very active field of orthogonal polynomials.
General Orthogonal Polynomials
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Author : Herbert Stahl
language : en
Publisher: Cambridge University Press
Release Date : 1992-04-24
General Orthogonal Polynomials written by Herbert Stahl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-24 with Mathematics categories.
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
Classical And Quantum Orthogonal Polynomials In One Variable
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Author : Mourad Ismail
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-21
Classical And Quantum Orthogonal Polynomials In One Variable written by Mourad Ismail and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-21 with Mathematics categories.
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Asymptotic Expansion Of A Partition Function Related To The Sinh Model
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Author : Gaëtan Borot
language : en
Publisher: Springer
Release Date : 2016-12-08
Asymptotic Expansion Of A Partition Function Related To The Sinh Model written by Gaëtan Borot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Science categories.
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.
Discrete Orthogonal Polynomials
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Author : J. Baik
language : en
Publisher: Princeton University Press
Release Date : 2007-01-02
Discrete Orthogonal Polynomials written by J. Baik and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-02 with Mathematics categories.
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Weighted Approximation With Varying Weight
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Author : Vilmos Totik
language : en
Publisher: Springer
Release Date : 2006-11-15
Weighted Approximation With Varying Weight written by Vilmos Totik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.