## Special Functions: Group Theoretical Aspects and ApplicationsR.A. Askey, Tom H. Koornwinder, Walter J. Schempp 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 |

305 | |

### Other editions - View all

Special Functions: Group Theoretical Aspects and Applications R. A. Askey,Tom H. Koornwinder,Walter J. Schempp No preview available - 2014 |

### Common terms and phrases

Abel transform Abelian addition formula Amer Anal analogue analytic Applications Askey basic hypergeometric Chebli Chevalley groups coefficients commuting compact complex corresponding decomposition defined denote differential operator discrete eigenfunctions eigenvalues explicit Faraut Flensted-Jensen Fourier transform func function f Gelfand pair GF(q given group G group theoretic Hahn polynomials Harm(k harmonic analysis Heisenberg group Helgason hypergeometric functions hypergeometric series identity integral intertwining functions invariant irreducible irrep isomorphic Jacobi functions Jacobi polynomials Jacobi transform K-finite Koornwinder Krawtchouk polynomials Laguerre lattice Lemma Let F Lie algebra linear mapping Math Mathematics matrix elements nilpotent nomials obtain operators on H orthogonal polynomials orthogonality relation Paley-Wiener Plancherel measure Plancherel theorem positive definite proof PV convolution operator rank result satisfies SIAM special functions spherical functions spherical harmonics subgroup subspace symmetric spaces tensor operators theory tions variables vector Weyl Wigner zero