Symmetric Functions And Orthogonal Polynomials

Author : Ian Grant Macdonald
Publisher : American Mathematical Soc.
ISBN 13 : 0821807706
Total Pages : 71 pages
Book Rating : 4.05/5 ( download)

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Download or read book Symmetric Functions and Orthogonal Polynomials written by Ian Grant Macdonald and published by American Mathematical Soc.. This book was released on 1998 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alain Lascoux
Publisher : American Mathematical Soc.
ISBN 13 : 0821828711
Total Pages : 282 pages
Book Rating : 4.17/5 ( download)

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Download or read book Symmetric Functions and Combinatorial Operators on Polynomials written by Alain Lascoux and published by American Mathematical Soc.. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ian Grant Macdonald
Publisher : Oxford University Press
ISBN 13 : 9780198504504
Total Pages : 496 pages
Book Rating : 4.00/5 ( download)

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Download or read book Symmetric Functions and Hall Polynomials written by Ian Grant Macdonald and published by Oxford University Press. This book was released on 1998 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Renato Alvarez-Nodarse
Publisher : Nova Publishers
ISBN 13 : 9781594540097
Total Pages : 222 pages
Book Rating : 4.98/5 ( download)

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Download or read book Laredo Lectures on Orthogonal Polynomials and Special Functions written by Renato Alvarez-Nodarse and published by Nova Publishers. This book was released on 2004 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Douglas Bowman
Publisher : American Mathematical Soc.
ISBN 13 : 082182774X
Total Pages : 73 pages
Book Rating : 4.41/5 ( download)

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Download or read book $q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions written by Douglas Bowman and published by American Mathematical Soc.. This book was released on 2002 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
ISBN 13 : 3540310622
Total Pages : 432 pages
Book Rating : 4.24/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions written by Francisco Marcellàn and published by Springer Science & Business Media. This book was released on 2006-06-19 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special 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.

Author : Charles F. Dunkl
Publisher : Cambridge University Press
ISBN 13 : 1316061906
Total Pages : 439 pages
Book Rating : 4.09/5 ( download)

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Download or read book Orthogonal Polynomials of Several Variables written by Charles F. Dunkl and published by Cambridge University Press. This book was released on 2014-08-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Gabor Szegš
Publisher : American Mathematical Soc.
ISBN 13 : 0821810235
Total Pages : 448 pages
Book Rating : 4.31/5 ( download)

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Download or read book Orthogonal Polynomials written by Gabor Szegš and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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.

Author : Diego Dominici
Publisher : American Mathematical Soc.
ISBN 13 : 0821846507
Total Pages : 226 pages
Book Rating : 4.06/5 ( download)

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Download or read book Special Functions and Orthogonal Polynomials written by Diego Dominici and published by American Mathematical Soc.. This book was released on 2008 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : Theodore S Chihara
Publisher : Courier Corporation
ISBN 13 : 0486141411
Total Pages : 276 pages
Book Rating : 4.11/5 ( download)

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Download or read book An Introduction to Orthogonal Polynomials written by Theodore S Chihara and published by Courier Corporation. This book was released on 2014-07-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. 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. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.