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Representation Theory and Noncommutative Harmonic Analysis II

Homogeneous Spaces, Representations and Special Functions

A.A. Kirillov (Herausgeber)

Buch | Hardcover

VIII, 270 Seiten

1995
Springer Berlin (Verlag)
978-3-540-54702-0 (ISBN)

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At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the prob ability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions. They are doubly periodic functions of a complex variable. This periodicity has led to consideration of the lattice of periods and to linear-fractional trans formations of the complex plane which leave this lattice invariant. The group of these transformations is isomorphic to the quotient group of the group 8L(2, Z) of unimodular matrices of the second order with integral elements with respect to its center. Investigation of properties of elliptic functions led to the study of automorphic functions and forms. This gave the first connec tion between the theory of groups and this important class of functions. The further development of the theory of automorphic functions was related to geometric concepts connected with the fact that the group of linear-fractional transformations with real elements can be realized as the group of motions of th the Lobachevskij plane. We also note that at the beginning of the 19 century Gauss used the group 8L(2, Z) in his papers on the theory of indeterminate quadratic forms.

I. Harmonic Analysis on Homogeneous Spaces.- II. Representations of Lie Groups and Special Functions.- Author Index.

Erscheint lt. Verlag	20.6.1995
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Co-Autor	A.U. Klimyk, V.F. Molchanov, N.Ya. Vilenkin
Übersetzer	G.van Dijk, A.U. Klimyk, V.F. Molchanov, S.Z. Pakuliak
Zusatzinfo	VIII, 270 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	532 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Calculus • Darstellungstheorie • Fourier transform • Fourier Transformation • Integraltransformation • integral transforms • Orthogonale Polynome • orthogonal polynomials • Poissonsche Transformation • poisson transform • Representation Theory • theoretical physics
ISBN-10	3-540-54702-9 / 3540547029
ISBN-13	978-3-540-54702-0 / 9783540547020
Zustand	Neuware