#### Lectures in mathematics : Kyoto University

##### vol. 7

Spherical functions and spherical matrix functions on locally compact groups / by Hitoshi Shin'ya

c1974

Introduction | 1 |

§ 1. Representations and their irreducibilities | 8 |

§ 2. Maximal ideals in L(G) and topologically irreducible nice representations | 14 |

§ 3. The multiplicities of irreducible representations of a compact subgroup | 19 |

§ 4. Spherical functions | 25 |

§ 5. Correspondence between representations and spherical functions | 47 |

§ 6. Irreducible representations of the algebra L^o(δ) and L(δ) | 52 |

§ 7. Spherical matrix functions | 56 |

§ 8. Spherical matrix functions on connected Lie groups | 64 |

§ 9. A construction of matrix functions on a group of type G = KS | 74 |

References | 90 |