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Author : Jean Dieudonné
Publisher : American Mathematical Soc.
Page : 65 pages
File Size : 47,8 Mb
Release : 1980
Category : Mathematics
ISBN : 9780821816929
Author : Jean Dieudonn
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 49,9 Mb
Release : 1980-12-31
Category : Mathematics
ISBN : 0821888870
Author : Naum I︠A︡kovlevich Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 48,6 Mb
Release : 1991-11-30
Category : Mathematics
ISBN : 0792314662
One service mathematici has rendered the 'Et moi, ... si j'avait IU comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belong., on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', Eric T. Bell able to do something with it. O. H eaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other pans and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'el;re of this series."
Author : N. Ja. Vilenkin,A. U. Klimyk
Publisher : Unknown
Page : 524 pages
File Size : 55,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401728860
Author : Naum I︠A︡kovlevich Vilenkin,Anatoliĭ Ulʹi︠a︡novich Klimyk
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 41,6 Mb
Release : 1995
Category : Mathematics
ISBN : 0792332105
The present book is a continuation of the three-volume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to Clebsch-Gordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics.
Author : N.Ja. Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 629 pages
File Size : 52,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401728836
This is the second of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of special functions and orthogonal polynomials (Legendre, Gegenbauer, Jacobi, Laguerre, Bessel and others) which are related to the class 1 representations of various groups. The tree method for the construction of bases for representation spaces is given. `Continuous' bases in the spaces of functions on hyperboloids and cones and corresponding Poisson kernels are found. Also considered are the properties of the q-analogs of classical orthogonal polynomials, related to representations of the Chevalley groups and of special functions connected with fields of p-adic numbers. Much of the material included appears in book form for the first time and many of the topics are presented in a novel way. This volume will be of great interest to specialists in group representations, special functions, differential equations with partial derivatives and harmonic anlysis. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.
Author : N.Ja. Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 651 pages
File Size : 53,8 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401728812
This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with q-analogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semi-simple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fand-Tsetlin basis, and, finally, modular forms, theta-functions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.
Author : Anonim
Publisher : Unknown
Page : 607 pages
File Size : 43,9 Mb
Release : 1993
Category : Electronic
ISBN : OCLC:1088828584
Author : Naum I︠A︡kovlevich Vilenkin,N.Ja. Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 51,5 Mb
Release : 1992-09-30
Category : Mathematics
ISBN : 079231493X
This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with q-analogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semi-simple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fand-Tsetlin basis, and, finally, modular forms, theta-functions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.
Author : E.B. Vinberg
Publisher : Birkhäuser
Page : 151 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892742
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
Author : Willard Miller
Publisher : American Mathematical Soc.
Page : 43 pages
File Size : 51,8 Mb
Release : 1964
Category : Lie algebras
ISBN : 9780821812501
Author : Naum Ja Vilenkin,Naum Âkovlevič Vilenkin,Anatolij U. Klimyk
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 1991
Category : Electronic
ISBN : OCLC:632617513
Author : Refaat El Attar
Publisher : Lulu.com
Page : 311 pages
File Size : 42,9 Mb
Release : 2005-12-06
Category : Technology & Engineering
ISBN : 9780557037636
(Hardcover). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.
Author : Richard Beals,Roderick Wong
Publisher : Cambridge University Press
Page : 128 pages
File Size : 52,6 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 9781139490436
The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.
Author : Dmitriĭ Petrovich Zhelobenko
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 51,6 Mb
Release : 1973-01-01
Category : Mathematics
ISBN : 0821886649