Orthogonal Polynomials For Exponential Weights

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Orthogonal Polynomials for Exponential Weights

Author : A. L. Levin
Publisher : Springer Science & Business Media
ISBN 13 : 9780387989419
Total Pages : 492 pages
Book Rating : 4.9/5 (894 download)

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Book Synopsis Orthogonal Polynomials for Exponential Weights by : A. L. Levin

Download or read book Orthogonal Polynomials for Exponential Weights written by A. L. Levin and published by Springer Science & Business Media. This book was released on 2001-06-29 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 book will be of interest to researchers in approximation theory, harmonic analysis, numerical analysis, potential theory, and all those that apply orthogonal polynomials.

Orthogonal Polynomials for Exponential Weights

Author : Eli Levin
Publisher : Springer Science & Business Media
ISBN 13 : 1461302013
Total Pages : 472 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Orthogonal Polynomials for Exponential Weights by : Eli Levin

Download or read book Orthogonal Polynomials for Exponential Weights written by Eli Levin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : A. L. Levin
Publisher : American Mathematical Soc.
ISBN 13 : 0821825992
Total Pages : 166 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ by : A. L. Levin

Download or read book Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ written by A. L. Levin and published by American Mathematical Soc.. This book was released on 1994 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Weighted Approximation with Varying Weight

Author : Vilmos Totik
Publisher : Springer
ISBN 13 : 3540483233
Total Pages : 119 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Weighted Approximation with Varying Weight by : Vilmos Totik

Download or read book Weighted Approximation with Varying Weight written by Vilmos Totik and published by Springer. This book was released on 2006-11-15 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Logarithmic Potentials with External Fields

Author : Edward B. Saff
Publisher : Springer Science & Business Media
ISBN 13 : 3662033291
Total Pages : 517 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Logarithmic Potentials with External Fields by : Edward B. Saff

Download or read book Logarithmic Potentials with External Fields written by Edward B. Saff and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.

Orthogonal Polynomials

Author : Paul Nevai
Publisher : Springer Science & Business Media
ISBN 13 : 9400905017
Total Pages : 472 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Orthogonal Polynomials by : Paul Nevai

Download or read book Orthogonal Polynomials written by Paul Nevai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.

Limit Theorems of Polynomial Approximation with Exponential Weights

Author : Michael I. Ganzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821840630
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Limit Theorems of Polynomial Approximation with Exponential Weights by : Michael I. Ganzburg

Download or read book Limit Theorems of Polynomial Approximation with Exponential Weights written by Michael I. Ganzburg and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.

Strong Asymptotics for Extremal Polynomials Associated with Weights on R

Author : Doron S. Lubinsky
Publisher : Springer
ISBN 13 : 3540388575
Total Pages : 160 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Strong Asymptotics for Extremal Polynomials Associated with Weights on R by : Doron S. Lubinsky

Download or read book Strong Asymptotics for Extremal Polynomials Associated with Weights on R written by Doron S. Lubinsky and published by Springer. This book was released on 2006-11-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Function Spaces

Author : K. Jarosz
Publisher : CRC Press
ISBN 13 : 9780824796655
Total Pages : 412 pages
Book Rating : 4.7/5 (966 download)

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Book Synopsis Function Spaces by : K. Jarosz

Download or read book Function Spaces written by K. Jarosz and published by CRC Press. This book was released on 1995-07-19 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the proceedings from the Second Conference on Function Spaces, this work details known results and fresh discoveries on a wide range of topics concerning function spaces. It covers advances in areas such as spaces and algebras of analytic functions, Lp-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.

General Orthogonal Polynomials

Author : Herbert Stahl
Publisher : Cambridge University Press
ISBN 13 : 9780521415347
Total Pages : 272 pages
Book Rating : 4.4/5 (153 download)

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Book Synopsis General Orthogonal Polynomials by : Herbert Stahl

Download or read book General Orthogonal Polynomials written by Herbert Stahl and published by Cambridge University Press. This book was released on 1992-04-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.

Asymptotics for Orthogonal Polynomials

Author : Walter Van Assche
Publisher : Springer
ISBN 13 : 354047711X
Total Pages : 207 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Asymptotics for Orthogonal Polynomials by : Walter Van Assche

Download or read book Asymptotics for Orthogonal Polynomials written by Walter Van Assche and published by Springer. This book was released on 2006-11-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.

Orthogonal Polynomials and Their Applications

Author : Jaime Vinuesa
Publisher : CRC Press
ISBN 13 : 9780824781613
Total Pages : 238 pages
Book Rating : 4.7/5 (816 download)

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Book Synopsis Orthogonal Polynomials and Their Applications by : Jaime Vinuesa

Download or read book Orthogonal Polynomials and Their Applications written by Jaime Vinuesa and published by CRC Press. This book was released on 1989-05-25 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Software Repository for Orthogonal Polynomials

Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611975220
Total Pages : 67 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis A Software Repository for Orthogonal Polynomials by : Walter Gautschi

Download or read book A Software Repository for Orthogonal Polynomials written by Walter Gautschi and published by SIAM. This book was released on 2018-03-20 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Software Repository for Orthogonal Polynomials is the first book that provides graphs and references to online datasets that enable the generation of a large number of orthogonal polynomials with classical, quasi-classical, and nonclassical weight functions. Useful numerical tables are also included. The book will be of interest to scientists, engineers, applied mathematicians, and statisticians.????

Orthogonal Polynomials and Painlevé Equations

Author : Walter Van Assche
Publisher : Cambridge University Press
ISBN 13 : 1108441947
Total Pages : 192 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Orthogonal Polynomials and Painlevé Equations by : Walter Van Assche

Download or read book Orthogonal Polynomials and Painlevé Equations written by Walter Van Assche and published by Cambridge University Press. This book was released on 2018 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of intriguing connections between Painlev equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlev equations.

Weighted Polynomial Approximation and Numerical Methods for Integral Equations

Author : Peter Junghanns
Publisher : Springer Nature
ISBN 13 : 303077497X
Total Pages : 662 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Weighted Polynomial Approximation and Numerical Methods for Integral Equations by : Peter Junghanns

Download or read book Weighted Polynomial Approximation and Numerical Methods for Integral Equations written by Peter Junghanns and published by Springer Nature. This book was released on 2021-08-10 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

Approximation Theory VIII

Author : Charles K. Chui
Publisher : World Scientific
ISBN 13 : 9814532592
Total Pages : 606 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Approximation Theory VIII by : Charles K. Chui

Download or read book Approximation Theory VIII written by Charles K. Chui and published by World Scientific. This book was released on 1995 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.

Approximation Theory Viii - Volume 1: Approximation And Interpolation

Author : Charles K Chui
Publisher : World Scientific
ISBN 13 : 9814549061
Total Pages : 606 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Approximation Theory Viii - Volume 1: Approximation And Interpolation by : Charles K Chui

Download or read book Approximation Theory Viii - Volume 1: Approximation And Interpolation written by Charles K Chui and published by World Scientific. This book was released on 1995-11-07 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.