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:
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.
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.
Download or read book Special Functions and the Theory of Group Representations written by Naum Ja Vilenkin and published by . This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Special Functions and the Theory of Group Representations written by Naum Âkovlevič Vilenkin and published by . This book was released on 1988 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Special Functions and the Theory of Group Representations written by and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Special functions and the theory of group representations written by Naum Jakovlevič Vilenkin and published by . This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representation of Lie Groups and Special Functions written by N. Ja. Vilenkin and published by . This book was released on 2014-01-15 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Group Representations written by M.A. Naimark and published by Springer. This book was released on 2011-11-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Group Theory in Physics written by Wu-Ki Tung and published by World Scientific. This book was released on 1985 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet.
Download or read book Special Functions written by James D. Talman and published by . This book was released on 1968 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In theoretical physics, routine use is made of many properties, such as recurrence relations and addition theorems, of the special functions of mathematical physics. These properties are for the most part classical, and their derivations are usually based on the methods of classical analysis. The purpose of this book is to show how these functions are also related to the theory of group representations and to derive their important properties from this theory. This approach elucidates the geometric background for the existence of the relations among the special functions. Moreover, the derivations may be more rationally motivated than are the usual complicated manipulations of power series, integral representations, and so on. I hope that the reader may find in this book reasonably simple derivations of many of the relations commonly used in theoretical physics for which the proofs may otherwise be somewhat unfamiliar. In order that the book be fairly self-contained, approximately the first third delves into a preliminary discussion of such topics as Lie groups, group representations, and so on. The remaining chapters are devoted to various groups, and the special functions are discussed in conjunction with the group with which it is associated. Because of the inclusion of the introductory material, the only prerequisite is a reasonable knowledge of linear algebra. The original impetus for the writing of this book was provided by a lecture course given by Professor Eugene P. Wigner a number of years ago. I am greatly indebted to Professor Wigner for his suggestion that I pursue the subject of the lectures further and for his continued friendly interest and advice in the work.-I wish to thank Dr. Trevor Luke for carefully checking the manuscript. I also wish to thank my wife, whose encouragement contributed greatly to the writing of the book.
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.
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%.
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 1995 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Special Functions and the Theory of Group Representations written by Naoum Iakovlevitch Vilenkine and published by . This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
