Vol. 103, No. 2, 1982

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
A Fourier transform theorem on nilmanifolds and nil-theta functions

Richard Cole Penney

Vol. 103 (1982), No. 2, 539–568
Abstract

A theorem describing the image of the Euclidean Fourier transform on certain nilmanifolds is proven. As an application, we compute the Fourier transform of a certain class of distributions on a manifold which is analogous with the class of classical theta functions on C. It is shown that our theta functions satisfy a functional equation which generalizes the functional equation satisfied by the Jacobi theta functions.

Mathematical Subject Classification 2000
Primary: 22E30
Secondary: 14K25, 22E25
Milestones
Received: 15 January 1980
Published: 1 December 1982
Authors
Richard Cole Penney