Inzell Lectures On Orthogonal Polynomials

Author : Wolfgang zu Castell
Publisher : Nova Publishers
Page : 416 pages
File Size : 53,9 Mb
Release : 2005
Category : Mathematics
ISBN : 1594541086

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Inzell Lectures on Orthogonal Polynomials by Wolfgang zu Castell Pdf

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 mathematical analysis. Deep connections between harmonic analysis and the theory of special functions have been discovered comparatively late, but since then have been exploited in many directions. The Inzell Lectures focus on the interrelation between orthogonal polynomials and harmonic analysis.

Author : Amilcar Jose Pinto Lopes Branquinho
Publisher : Nova Publishers
Page : 250 pages
File Size : 49,9 Mb
Release : 2008
Category : Mathematics
ISBN : 1600219721

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Coimbra Lecture Notes on Orthogonal Polynomials by Amilcar Jose Pinto Lopes Branquinho Pdf

Orthogonal Polynomials and Special Functions (OPSF) have a very rich history, going back to 19th century when mathematicians and physicists tried to solve the most important deferential equations of mathematical physics. Hermite-Padé approximation was also introduced at that time, to prove the transcendence of the remarkable constant e (the basis of the natural logarithm). Since then OPSF has developed to a standard subject within mathematics, which is driven by applications. The applications are numerous, both within mathematics (e.g. statistics, combinatory, harmonic analysis, number theory) and other sciences, such as physics, biology, computer science, chemistry. The main reason for the fact that OPSF has been so successful over the centuries is its usefulness in other branches of mathematics and physics, as well as other sciences. There are many different aspects of OPSF. Some of the most important developments for OPSF are related to the theory of rational approximation of analytic functions, in particular the extension to simultaneous rational approximation to a system of functions. Important tools for rational approximation are Riemann-Hilbert problems, the theory of orthogonal polynomials, logarithmic potential theory, and operator theory for difference operators. This new book presents the latest research in the field.

Author : Francisco Marcellàn,Walter Van Assche
Publisher : Springer
Page : 422 pages
File Size : 48,7 Mb
Release : 2006-10-18
Category : Mathematics
ISBN : 9783540367161

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Orthogonal Polynomials and Special Functions by Francisco Marcellàn,Walter Van Assche Pdf

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.

Author : Howard S. Cohl,Mourad E. H. Ismail
Publisher : Cambridge University Press
Page : 351 pages
File Size : 51,6 Mb
Release : 2020-10-15
Category : Mathematics
ISBN : 9781108821599

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Lectures on Orthogonal Polynomials and Special Functions by Howard S. Cohl,Mourad E. H. Ismail Pdf

Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.

Author : Richard Askey
Publisher : SIAM
Page : 117 pages
File Size : 42,7 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 1611970474

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Orthogonal Polynomials and Special Functions by Richard Askey Pdf

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 of univalent functions, by applications to quadrature problems, and theorems on the location of zeros of trigonometric polynomials. There are also applications to combinatorial problems, statistics, and physical problems.

Author : Renato Alvarez-Nodarse,Francisco Marcellán,Walter van Assche
Publisher : Nova Publishers
Page : 222 pages
File Size : 40,6 Mb
Release : 2004
Category : Mathematics
ISBN : 1594540098

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Laredo Lectures on Orthogonal Polynomials and Special Functions by Renato Alvarez-Nodarse,Francisco Marcellán,Walter van Assche Pdf

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 orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.

Author : L szl¢ Sz‚kelyhidi
Publisher : World Scientific
Page : 210 pages
File Size : 42,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814407014

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Functional Equations on Hypergroups by L szl¢ Sz‚kelyhidi Pdf

The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate OC marriageOCO where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods OCo and, sometimes, a new world of unexpected difficulties.

Author : Charles F. Dunkl,Yuan Xu
Publisher : Cambridge University Press
Page : 439 pages
File Size : 50,5 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781107071896

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Orthogonal Polynomials of Several Variables by Charles F. Dunkl,Yuan Xu Pdf

Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.

Author : Erik Koelink,Walter Van Assche
Publisher : Springer
Page : 250 pages
File Size : 48,9 Mb
Release : 2003-07-03
Category : Mathematics
ISBN : 9783540449454

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Orthogonal Polynomials and Special Functions by Erik Koelink,Walter Van Assche Pdf

The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.

Author : Gábor Szegő
Publisher : Unknown
Page : 424 pages
File Size : 45,6 Mb
Release : 1939
Category : Functions, Orthogonal
ISBN : UGA:32108006366218

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Orthogonal Polynomials by Gábor Szegő Pdf

Author : Herbert Heyer,Gyula Pap
Publisher : World Scientific
Page : 425 pages
File Size : 41,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814282482

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Structural Aspects in the Theory of Probability by Herbert Heyer,Gyula Pap Pdf

The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.

Author : Anonim
Publisher : Unknown
Page : 980 pages
File Size : 43,9 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015067193329

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Mathematical Reviews by Anonim Pdf

Author : Theodore S Chihara
Publisher : Courier Corporation
Page : 276 pages
File Size : 54,7 Mb
Release : 2011-02-17
Category : Mathematics
ISBN : 9780486479293

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An Introduction to Orthogonal Polynomials by Theodore S Chihara Pdf

"This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--

Author : Ian Grant Macdonald
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 50,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821807705

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Symmetric Functions and Orthogonal Polynomials by Ian Grant Macdonald Pdf

One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

Author : Walter Gautschi
Publisher : SIAM
Page : 335 pages
File Size : 46,8 Mb
Release : 2016-05-23
Category : Science
ISBN : 9781611974300

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Orthogonal Polynomials in MATLAB by Walter Gautschi Pdf

Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 or so years.?Orthogonal Polynomials in MATLAB: Exercises and Solutions?describes these techniques and related applications, all supported by MATLAB programs, and presents them in a unique format of exercises and solutions designed by the author to stimulate participation. Important computational problems in the physical sciences are included as models for readers to solve their own problems.?