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Fourier series and orthogonal polynomials
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Dunham Jackson
This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, ...
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Orthogonal Polynomials and Continued Fractions: From Euler's Point of View
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Sergey Khrushchev
Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions ...
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Discrepancy of Signed Measures and Polynomial Approximation
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Vladimir V Andrievskii, Hans-Peter Blatt
The book is an authoritative and up-to-date introduction to the field of Analysis and Potential Theory dealing with the distribution of zeros of classical systems of polynomials such as orthogonal polynomials, Chebyshev, Fekete and Bieberbach polynomials, best or near-best approximating polynomials on compacts sets and on the real line. The main ...
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Double Affine Hecke Algebras
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by
Ivan Cherednik
This is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is ...
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Orthogonal Polynomials for Exponential Weights
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by
A L Levin, Eli Levin, Doron S Lubinsky
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 ...
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Handbook of Computational Methods for Integration
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Michael R Schaferkotter, Prem K Kythe
During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open ...
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Orthogonal polynomials and their applications proceedings of the international congress
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Vinuesa
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Approximation and Computation: A Festschrift in Honor of Walter Gautschi
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by
R. V. M. Zahar (Editor)
In recognition of Walter Gautschi's many contributions to mathematics and computer science, and to celebrate his 65th birthday, an international conference was held in his honour at Purdue University in December 1993. These papers are taken from that conference. This book provides a survey of current topics in the fields of approximation, ...
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Stochastic Processes and Orthogonal Polynomials
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by
Wim Schoutens
The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic analysis for birth-death processes and ...
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Orthogonal Polynomials
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by
Gabor Szego
Unknown function: Szego
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Discrete Orthogonal Polynomials: Asymptotics and Applications
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by
J Baik, T Kriecherbauer, K T -R McLaughlin
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. ...
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Orthogonal Polynomials of Several Variables
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by
Charles F Dunkl, Yuan Xu, G -C Rota (Editor)
This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate analysis, including approximations and numerical integration. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and ...
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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
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by
Percy Deift
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ...
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Orthogonal Polynomials: Computation and Approximation
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by
Walter Gautschi
This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are ...
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Inzell Lectures on Orthogonal Polynomials
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by
Wolfgang Zu Castell, Frank Filbir, Brigitte Forster
Based on the success of Fourier analysis and Hilbert space theory, orthogonal expansions undoubtedly count as fundamental concepts of mathematical analysis. Along with the need for highly involved functions systems having special properties and analysis on more complicated domains, harmonic analysis has steadily increased its importance in modern ...
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Classical and Quantum Orthogonal Polynomials in One Variable
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by
Mourad E H Ismail
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. Its encyclopedic coverage includes classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those discovered over the last 50 years, e.g. Askey-Wilson and Al-Salam-Chihara ...
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Orthogonal polynomials and special functions
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by
Richard Askey
Originally presented as lectures, the theme of this volume is that one studies orthogonal polynomials and special functions not for their own sake, but to be able to use them to solve problems. The author presents problems suggested by the isometric embedding of projective spaces in other projective spaces, by the desire to construct large classes ...
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General Orthogonal Polynomials
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by
Stahl, Totik
In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on the complex plane. In the development of the theory, the main emphasis is on asymptotic ...
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Power Orthogonal Polynomials
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by
Ying Guang Shi
In this book, the first chapter lists the basic results of orthogonal polynomials, Jacobi, Laguerre, and Hermite polynomials, and collects some frequently used theorems and formulas. As a base and useful tool, the representation and quantitative theory of Hermite interpolation is the subject of Chapter 2. The theory of power orthogonal polynomials ...
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Orthogonal Polynomials in Two Variables
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by
P K Suetin, Suetin K Suetin
Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two ...
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Polynomes Orthogonaux Formels - Applications
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by
A Draux
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Applications and Computation of Orthogonal Polynomials: Conference in Oberwolfach, March 22-28, 1998
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by
Walter Gautschi (Editor), Professor Gene H Golub (Editor), Gerhard Opfer (Editor)
This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation. The applications address problems in applied mathematics as well as problems in engineering and the sciences. Prominent among the former are least-squares approximations, Gauss and related quadrature, iterative methods ...
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Introduction to the Theory of Weighted Polynomial Approximation
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by
H. N. Mhaskar
The book starts with an introduction to the general theory of orthogonal polynomials, proving elementary facts about such polynomials in general. Chapter 2 deals with standard results in the theory of trigonometric approximation, such as the Jackson and Bernstein-Stechkin theorems in a novel way, which is more suitable to understand the techniques ...
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Q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions
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by
Douglas Bowman
In this work, we explore ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic ...
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Laredo Lectures on Orthogonal Polynomials and Special Functions: Focus on the Theory of Special Functions and Orthogonal Polynomials: In "Advances in the Theory of Special Functions and Orthogonal Polynomials"
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by
Francisco Marcellan
This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for ...
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