Vol. 55, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Groups of matrices acting on distribution spaces

Sav Roman Harasymiv

Vol. 55 (1974), No. 2, 403–417
Abstract

Let E be a locally convex space of temperate distributions on the n-dimensional Euclidean space Rn, and G a closed subgroup of Gl(n,R), the general linear group over Rn. An attempt is made to identify those distributions which can be approximated in E by linear combinations of distributions of the form u(Ax + b), where u is a fixed element of E, A varies over G, and b varies over Rn. A cancellation theorem is proved; this then allows the support of the Fourier transform of any annihilator of the set of distributions of the form u(Ax + b) to be localized. This in turn is used to obtain approximation results.

Mathematical Subject Classification 2000
Primary: 46F10
Milestones
Received: 6 June 1973
Revised: 24 January 1974
Published: 1 December 1974
Authors
Sav Roman Harasymiv