Representation Of Lie Groups And Special Functions

Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 9401728852
Total Pages : 518 pages
Book Rating : 4.50/5 ( download)

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Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.

Author : Naum I︠A︡kovlevich Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 9780792314660
Total Pages : 650 pages
Book Rating : 4.62/5 ( download)

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Download or read book Representation of Lie Groups and Special Functions written by Naum I︠A︡kovlevich Vilenkin and published by Springer Science & Business Media. This book was released on 1991-11-30 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886526
Total Pages : 628 pages
Book Rating : 4.25/5 ( download)

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Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1978 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 940172881X
Total Pages : 651 pages
Book Rating : 4.12/5 ( download)

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Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821815724
Total Pages : 613 pages
Book Rating : 4.25/5 ( download)

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Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.

Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 940113538X
Total Pages : 635 pages
Book Rating : 4.82/5 ( download)

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Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first 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 classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers.

Author : Jean Dieudonné
Publisher : American Mathematical Soc.
ISBN 13 : 0821816926
Total Pages : 65 pages
Book Rating : 4.29/5 ( download)

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Download or read book Special Functions and Linear Representations of Lie Groups written by Jean Dieudonné and published by American Mathematical Soc.. This book was released on 1980 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A.A. Kirillov
Publisher : Springer Science & Business Media
ISBN 13 : 3662097567
Total Pages : 274 pages
Book Rating : 4.64/5 ( download)

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Download or read book Representation Theory and Noncommutative Harmonic Analysis II written by A.A. Kirillov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.

Author :
Publisher :
ISBN 13 :
Total Pages : 607 pages
Book Rating : 4.84/5 ( download)

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Download or read book Representation of Lie Groups and Special Functions Volume 2: Class I Representations, Special Functions, and Integral Transforms written by and published by . This book was released on 1993 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.98/5 ( download)

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Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples