Special Functions: Group Theoretical Aspects and Applications

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R.A. Askey, Tom H. Koornwinder, Walter J. Schempp
Springer Science & Business Media, Sep 30, 1984 - Mathematics - 352 pages
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Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
 

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Contents

JACOBI FUNCTIONS AND ANALYSIS ON NONCOMPACT SEMISIMPLE LIE GROUPS
1
ORTHOGONAL POLYNOMIALS AND CHEVALLEY GROUPS
87
SPECIAL FUNCTIONS AND GROUP THEORY IN THEORETICAL PHYSICS
129
LATTICE GAUGE THEORY ORTHOGONAL POLYNOMIALS AND qHYPERGEOMETRIC FUNCTIONS
163
THE LAGUERRE CALCULUS ON THE HEISENBERG GROUP
189
RADAR AMBIGUITY FUNCTIONS NILPOTENT HARMONIC ANALYSIS AND HOLOMORPHIC THETA SERIES
217
A FACTORIZATION THEOREM FOR THE FOURIER TRANSFORM OF A SEPARABLE LOCALLY COMPACT ABELIAN GROUP
261
BAND AND TIME LIMITING RECURSION RELATIONS AND SOME NONLINEAR EVOLUTION EQUATIONS
271
HARMONICS AND COMBINATORICS
287
Subject Index
305
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