Special Functions: Group Theoretical Aspects and Applications

1. Front Matter

   Pages i-xxxiv

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2. Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups

   • Tom H. Koornwinder

   Pages 1-85

3. Orthogonal Polynomials and Chevalley Groups

   • Dennis Stanton

   Pages 87-128

4. Special Functions and Group Theory in Theoretical Physics

   • L. C. Biedenharn, R. A. Gustafson, M. A. Lohe, J. D. Louck, S. C. Milne

   Pages 129-162

5. Lattice Gauge Theory, Orthogonal Polynomials and q-Hypergeometric Functions

   • George E. Andrews, Enrico Onofri

   Pages 163-188

6. The Laguerre Calculus on the Heisenberg Group

   • R. W. Beals, P. C. Greiner, J. Vauthier

   Pages 189-216

7. Radar Ambiguity Functions, Nilpotent Harmonic Analysis, and Holomorphic Theta Series

   • Walter Schempp

   Pages 217-260

8. A Factorization Theorem for the Fourier Transform of a Separable Locally Compact Abelian Group

   • Louis Auslander

   Pages 261-269

9. Band and Time Limiting, Recursion Relations and Some Nonlinear Evolution Equations

   • F. Alberto Grünbaum

   Pages 271-286

10. Harmonics and Combinatorics

    • J. J. Seidel

    Pages 287-303

11. Back Matter

    Pages 305-313

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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.

• calculus
• filtering
• harmonic analysis
• Hypergeometric function
• integrable system
• measure
• measure theory
• orthogonal polynomials
• special function

`This book will become useful and important, not just as a handy place to locate a reference, but for the many thought-provoking ideas generously provided by the authors.'
Foundations of Physics, 16:9 (1986)

• Mathematics Department, University of Wisconsin, Madison, USA

  R. A. Askey

• Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

  T. H. Koornwinder

• Department of Mathematics, University of Siegen, Germany

  W. Schempp

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