Symmetric Functions And Orthogonal Polynomials
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Symmetric Functions And Orthogonal Polynomials
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Author : Ian Grant Macdonald
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Symmetric Functions And Orthogonal Polynomials written by Ian Grant Macdonald and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
Symmetric Functions And Combinatorial Operators On Polynomials
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Author : Alain Lascoux
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Symmetric Functions And Combinatorial Operators On Polynomials written by Alain Lascoux and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Polynomials categories.
The theory of symmetric functions is an old topic in mathematics, which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and its occurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods, or the method of Cauchy and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.
Symmetric Functions And Hall Polynomials
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Author : Ian Grant Macdonald
language : en
Publisher: Oxford University Press
Release Date : 1998
Symmetric Functions And Hall Polynomials written by Ian Grant Macdonald and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and so on. Macdonald polynomials have become a part of basic material that a researcher simply must know if (s)he wants to work in one of the above domains, ensuring this new edition will appeal to a very broad mathematical audience. Featuring a new foreword by Professor Richard Stanley of MIT.
Q Difference Operators Orthogonal Polynomials And Symmetric Expansions
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Author : Douglas Bowman
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Q Difference Operators Orthogonal Polynomials And Symmetric Expansions written by Douglas Bowman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The author explores 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 properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future
Laredo Lectures On Orthogonal Polynomials And Special Functions
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Author : Renato Alvarez-Nodarse
language : en
Publisher: Nova Publishers
Release Date : 2004
Laredo Lectures On Orthogonal Polynomials And Special Functions written by Renato Alvarez-Nodarse and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Orthogonal Polynomials And Special Functions
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Author : Francisco Marcellàn
language : en
Publisher: Springer
Release Date : 2006-10-18
Orthogonal Polynomials And Special Functions written by Francisco Marcellàn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-18 with Mathematics categories.
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.
Special Functions And Orthogonal Polynomials
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Author : Diego Dominici
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Special Functions And Orthogonal Polynomials written by Diego Dominici and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.
Orthogonal Polynomials Of Several Variables
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Author : Charles F. Dunkl
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-21
Orthogonal Polynomials Of Several Variables written by Charles F. Dunkl 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 2014-08-21 with Mathematics categories.
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Macdonald Polynomials
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Author : Masatoshi Noumi
language : en
Publisher: Springer Nature
Release Date :
Macdonald Polynomials written by Masatoshi Noumi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Orthogonal Polynomials Of Several Variables
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Author : Charles F. Dunkl
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-21
Orthogonal Polynomials Of Several Variables written by Charles F. Dunkl 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 2014-08-21 with Mathematics categories.
Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.
