Vol. 102, No. 2, 1982

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
μ-theta functions

William George Frederick

Vol. 102 (1982), No. 2, 293–327

Using the technique of compact rational subgroup approximations to unitary representations on a nilmanifold, we justify the evaluation of a distribution at certain rational points of a group. This method allows us to give meaning to a distributional identity between theta-like functions at discrete points in the group. The identity itself arises from the equivalence of certain representations of the group. In attempting to compute an intertwining constant that is present, we are also able to show the existence of distributions that behave like the classical gaussians, i.e., they are eigenfunctions of the Fourier transform.

Mathematical Subject Classification 2000
Primary: 22E27
Received: 9 December 1980
Published: 1 October 1982
William George Frederick