Discrete Orthogonal Polynomials. (AM-164)
Author: Jinho Baik
Publisher: Princeton University Press
Published: 2007
Total Pages: 178
ISBN-13: 0691127344
DOWNLOAD EBOOKPublisher description
Posts
Frontiers In Orthogonal Polynomials And Q-series
Author: M Zuhair Nashed
Publisher: World Scientific
Published: 2018-01-12
Total Pages: 577
ISBN-13: 981322889X
DOWNLOAD EBOOKThis volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.
Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
Author: Percy Deift
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 273
ISBN-13: 0821826956
DOWNLOAD EBOOKThis 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 ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Orthogonal Polynomials
Author: Gabor Szeg
Publisher: American Mathematical Soc.
Published: 1939-12-31
Total Pages: 448
ISBN-13: 0821810235
DOWNLOAD EBOOKThe 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.
General Orthogonal Polynomials
Author: Herbert Stahl
Publisher: Cambridge University Press
Published: 1992-04-24
Total Pages: 272
ISBN-13: 9780521415347
DOWNLOAD EBOOKAn encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
Classical and Quantum Orthogonal Polynomials in One Variable
Author: Mourad Ismail
Publisher: Cambridge University Press
Published: 2005-11-21
Total Pages: 748
ISBN-13: 9780521782012
DOWNLOAD EBOOKThe first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights
Author: Eli Levin
Publisher: Springer
Published: 2018-02-13
Total Pages: 168
ISBN-13: 3319729470
DOWNLOAD EBOOKThis 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.
Asymptotics for Orthogonal Polynomials
Author: Walter Van Assche
Publisher: Springer
Published: 2006-11-14
Total Pages: 207
ISBN-13: 354047711X
DOWNLOAD EBOOKRecently 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 Special Functions
Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
Published: 2006-06-19
Total Pages: 432
ISBN-13: 3540310622
DOWNLOAD EBOOKSpecial functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.
Harmonic Analysis and Applications
Author: Carlos E. Kenig
Publisher: American Mathematical Soc.
Published: 2020-12-14
Total Pages: 345
ISBN-13: 1470461277
DOWNLOAD EBOOKThe origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
