Special Functions: Group Theoretical Aspects and Applications

✍ Scribed by Tom H. Koornwinder (auth.), R. A. Askey, T. H. Koornwinder, W. Schempp (eds.)

• Publisher: Springer Netherlands
• Year: 1984
• Tongue: English
• Leaves: 342
• Series: Mathematics and Its Applications 18
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxxiv
Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups....Pages 1-85
Orthogonal Polynomials and Chevalley Groups....Pages 87-128
Special Functions and Group Theory in Theoretical Physics....Pages 129-162
Lattice Gauge Theory, Orthogonal Polynomials and q-Hypergeometric Functions....Pages 163-188
The Laguerre Calculus on the Heisenberg Group....Pages 189-216
Radar Ambiguity Functions, Nilpotent Harmonic Analysis, and Holomorphic Theta Series....Pages 217-260
A Factorization Theorem for the Fourier Transform of a Separable Locally Compact Abelian Group....Pages 261-269
Band and Time Limiting, Recursion Relations and Some Nonlinear Evolution Equations....Pages 271-286
Harmonics and Combinatorics....Pages 287-303
Back Matter....Pages 305-313

✦ Subjects

Analysis