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Representation Theory and Noncommutative Harmonic Analysis II

  • Fester Einband
  • 280 Seiten
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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.


This volume of the Encyclopaedia contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F.Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N.Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semi-simple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to special functions, orthogonal polynomials and integral transforms. Both contributions are surveys introducing readers to the above topics 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.

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


Titel: Representation Theory and Noncommutative Harmonic Analysis II
Untertitel: Homogeneous Spaces, Representations and Special Functions
EAN: 9783540547020
ISBN: 3540547029
Format: Fester Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 280
Gewicht: 588g
Größe: H241mm x B160mm x T20mm
Jahr: 1995
Auflage: 1995

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