Smooth cuspidal automorphic forms and integrable discrete series
Abstract
In this paper we construct smooth cuspidal automorphic forms related to integrable discrete series of a connected semisimple Lie group with finite center for classical and adelic situation as an application of the theory of Schwartz spaces for automorphic forms developed by Casselman. In the classical situation, smooth cuspidal automorphic forms are constructed via an explicit continuous map from the Frech\' et space of smooth vectors of a Banach realization inside of an integrable discrete series into the space of smooth vectors of a strong topological dual of an appropriate Schwartz space.
Keywords
Cite
@article{arxiv.1610.05483,
title = {Smooth cuspidal automorphic forms and integrable discrete series},
author = {Goran Muić},
journal= {arXiv preprint arXiv:1610.05483},
year = {2016}
}
Comments
In Section 5 we added Lemma 5.3 about smooth matrix coefficients which gives a more precise description of smooth vectors in the Banach realization of integrable discrete series