Representation of Lie Groups and Special Functions Recent Advances - Vilenkin, Naum Ja. 1920-1991 (Springer Netherlands, 1995)
In 1991-1993 our three-volume book "Representation of Lie Groups and Special 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 representations. 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 generalizations of classical special functions that were dictated by matrix elements of representations
Keywords: Mathematics; Topological Groups; Harmonic analysis; Functions, special; Special Functions; Topological Groups, Lie Groups; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Abstract Harmonic Analysis; Mathematik; Lie-Gruppe; Darstellungstheorie; Darstellung -- Mathematik; Spezielle Funktion