Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the boundedness and unboundedness of certain convolution operators on nilpotent Lie groups


Author: Roe Goodman
Journal: Proc. Amer. Math. Soc. 39 (1973), 409-413
MSC: Primary 22E30
DOI: https://doi.org/10.1090/S0002-9939-1973-0320227-0
MathSciNet review: 0320227
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: One method of proving irreducibility of the ``principal series'' representations of semisimple Lie groups involves showing that a certain nonintegrable function on a nilpotent subgroup $ X$ cannot be regularized to give a bounded convolution operator on $ {L_2}(X)$. This note gives an elementary proof of this unboundedness property for the groups $ X$ which occur in real-rank one semisimple groups.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E30

Retrieve articles in all journals with MSC: 22E30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0320227-0
Article copyright: © Copyright 1973 American Mathematical Society