Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 2 (2019), 471-513.
The notion of cusp forms for a class of reductive symmetric spaces of split rank
We study a notion of cusp forms for the symmetric spaces with and . We classify all minimal parabolic subgroups of for which the associated cuspidal integrals are convergent and discuss the possible definitions of cusp forms. Finally, we show that the closure of the direct sum of the discrete series representations of coincides with the space of cusp forms.
Kyoto J. Math., Volume 59, Number 2 (2019), 471-513.
Received: 26 January 2016
Accepted: 3 April 2017
First available in Project Euclid: 9 May 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 22E46: Semisimple Lie groups and their representations 43A80: Analysis on other specific Lie groups [See also 22Exx]
van den Ban, Erik P.; Kuit, Job J.; Schlichtkrull, Henrik. The notion of cusp forms for a class of reductive symmetric spaces of split rank $1$. Kyoto J. Math. 59 (2019), no. 2, 471--513. doi:10.1215/21562261-2019-0015. https://projecteuclid.org/euclid.kjm/1557367351