## Harmonic Analysis on Homogeneous Spaces |

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### Contents

The theory of characters and the discrete series for semisimple Lie groups | 45 |

Functions on symmetric spaces | 101 |

Quantization and representation theory | 147 |

Copyright | |

29 other sections not shown

### Common terms and phrases

action acts admissible Amer analysis associated assume boundary bounded called Cartan character classifications closed compact complex compute condition connected consider constant construction contains continuous converges corresponding decomposition defined definition denote determined differential discrete series distribution elements equivalent example exists extends fact finite formula Fourier given gives Harish-Chandra harmonic Hence holomorphic implies induced integral invariant irreducible LEMMA Let G Lie algebra linear locally Math Mathematical maximal means measure method Moreover natural normal obtain operator orbit Plancherel Plancherel measure positive principal problem proof properties PROPOSITION prove reductive regular representation representation of G respect restriction root satisfies semisimple Lie groups solvable spherical functions square-integrable structure subgroup subgroup of G Suppose Theorem theory transform unique UNIVERSITY values vector write