## 1980 Seminar on Harmonic Analysis |

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### Contents

Lecture Course | 1 |

AUTOMORPRIC REPRESENTATIONS AND NUMBER TREORY | 3 |

of Semisimple Lie Groups | 53 |

Embedding Limits of Discrete Series of Semisimple Lie Groups | 55 |

The C Chevalleys Theorem | 65 |

Lpackets for SL | 69 |

ON HARMONIC FUNCTIONS ON SYMMETRIC SPACES AND BUILDINGS | 79 |

Discrete Series Character Identities and Fourier Inversion | 93 |

L boundedness of pseudodifferential operators | 135 |

An elementary proof of the theorem | 153 |

SZEGOS TBEOREM AND PSEUDODIFFERENTIAL OPERATORS | 165 |

Harmonic Analysis | 175 |

Some good and had characters I have known and where they led Harmonic analysis and functional equations | 177 |

Multilinear Grothendieck inequalities via the Schur algorithm by John JF Fournier 1 Introduction | 189 |

BURNS IDE TYPE THEOREMS FOR BANACB REPRESENTATIONS OF MOTION GROUPS AND ALGEBRAS | 213 |

Interpolation of Quasinormed Spaces Involving Weights | 245 |

L2C0R0MOLOGY AND LIE ALGEBRA COBOMOLOGY | 99 |

RGROUP AND ORBITS | 113 |

ON NONgANISRING OF LFUNCTIONS FOR GLn F Shahidi | 117 |

and Pseudodifferential Operators | 123 |

ROROSPHERICAL FUNCTIONS ON SWflETRIC SPACES | 125 |

Entire functions of exponential type as multipliers for weight functions | 269 |

A function that does not operate Michael A Rains | 279 |

FRACTIONAL MAXIMAL OPERATORS | 283 |

### Common terms and phrases

abelian group ahove Amarican Mathematical analytic continuation automorphic representation Banach algebra Banach representation Banach space boundedness Burnside type theorem character cohomology commutative complex condition Conference Proceedings volume conjecture conjugacy classes conoected constant construction converges corresponding Corvallis proceedings cubes Q decomposition defined denote discrete series representation dual element exponential type finite dimensional follows formula function f functional equation given Grothendieck group algebra group G harmonic analysis harmonic functions homomorphism houndary hounded implies induced representations inequality integral invariant irreducible representation isomorphic kernel L-functions L-packets Langlands Lemma Let G Lie algebra limits of discrete Math maximal modulo motion groups multiplicity nilpotent number theory obtain orbits pair polynomial principal series principal series representation proved pseudo-differential operators Rarish-Chandra representation of G representation tt restriction result root satisfies sequence solution subalgebra subgroup of G subset subspace Suppose symbols symmetric spaces unitary vector weight Weyl group

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Page v - This research was supported by a grant from the Natural Science and Engineering Research Council of Canada.