Special Functions and the Theory of Group Representations
N. Ja. Vilenkin, Наум Яковлевич Виленкин
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.
Категорії:
Том:
22
Рік:
1968
Видання:
Revised
Видавництво:
American Mathematical Society
Мова:
english
Сторінки:
613
ISBN 10:
0821815725
ISBN 13:
9780821815724
Серії:
Translations of Mathematical Monographs
Файл:
DJVU, 9.22 MB
IPFS:
,
english, 1968