## Boundary behaviour of limits of discrete series representations |

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### Contents

2 Notation and Preliminaries | 13 |

3 Schmids Operator 0 for G | 19 |

4 The Parabolic Subgroup P MAN | 25 |

16 other sections not shown

### Common terms and phrases

A^-dominant action of G Ad(u belonging to weight boundary value Cartan subgroup compact Cartan subalgebra compact Cartan subgroup compact root constant term continuous series corresponding cusp form defined differentiable discrete series representation dominant Eisenstein integrals element embedding epH(x equivalent follows function given Harish-Chandra parameter highest weight vector infinitesimal character integral form intertwining operator irreducible representation Iwasawa decomposition K-finite K-finite vectors K-type kernel Knapp and Wallach Lemma Let denote Lie algebra Lie group limits of discrete noncompact root nonsingular notation P-continuous series representation parabolic subgroup positive roots principal series representation Proof real rank representation of G representation space right hand side scalar Schmid's operator strongly orthogonal subgroup of G Suppose Szego integral Szego map Theorem ti(A tion Weyl chamber Weyl group x e G