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Author : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
Page : 628 pages
File Size : 51,5 Mb
Release : 1978
Category : Mathematics
ISBN : 0821886525
Author : Naum Ja Vilenkin
Publisher : Unknown
Page : 613 pages
File Size : 41,6 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:472247348
Author : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
Page : 613 pages
File Size : 48,7 Mb
Release : 1968
Category : Mathematics
ISBN : 0821815725
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 : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 45,5 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:802897199
Author : Naum Âkovlevič Vilenkin
Publisher : Unknown
Page : 613 pages
File Size : 47,5 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:468307767
Author : N.Ja. Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 49,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401728850
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 Jakovlevič Vilenkin
Publisher : Unknown
Page : 613 pages
File Size : 49,6 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:468307767
Author : Naum I︠A︡kovlevich Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 47,5 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 : Jean Dieudonné
Publisher : American Mathematical Soc.
Page : 65 pages
File Size : 46,7 Mb
Release : 1980
Category : Mathematics
ISBN : 9780821816929
Author : N.Ja. Vilenkin,A.U. Klimyk
Publisher : Springer Science & Business Media
Page : 635 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401135382
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 : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 43,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Author : M.A. Naimark,A.I Stern
Publisher : Springer
Page : 0 pages
File Size : 41,5 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 1461381444
Author's Preface to the Russian Edition This book is written for advanced students, for predoctoral graduate stu dents, and for professional scientists-mathematicians, physicists, and chemists-who desire to study the foundations of the theory of finite dimensional representations of groups. We suppose that the reader is familiar with linear algebra, with elementary mathematical analysis, and with the theory of analytic functions. All else that is needed for reading this book is set down in the book where it is needed or is provided for by references to standard texts. The first two chapters are devoted to the algebraic aspects of the theory of representations and to representations of finite groups. Later chapters take up the principal facts about representations of topological groups, as well as the theory of Lie groups and Lie algebras and their representations. We have arranged our material to help the reader to master first the easier parts of the theory and later the more difficult. In the author's opinion, however, it is algebra that lies at the heart of the whole theory. To keep the size of the book within reasonable bounds, we have limited ourselves to finite-dimensional representations. The author intends to devote another volume to a more general theory, which includes infinite dimensional representations.
Author : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 42,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662097564
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 : Jean Dieudonn
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 40,8 Mb
Release : 1980-12-31
Category : Mathematics
ISBN : 0821888870
Author : N. Ja. Vilenkin,A. U. Klimyk
Publisher : Unknown
Page : 524 pages
File Size : 45,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401728860
