Vol. 31, No. 2, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Dilations of rapidly decreasing functions

Sav Roman Harasymiv

Vol. 31 (1969), No. 2, 395–402
Abstract

Let S be the space of rapidly decreasing indefinitely differentiable functions on the n-dimensional Euclidean space Rn, and suppose that ϕ S. We attempt to characterize the closed vector subspace of S which is generated by the set of all functions of the form

(x1,⋅⋅⋅ ,xn) → ϕ(a1x1 + b1,⋅⋅⋅ ,aniljn + bn)

where a1,,an,b1,,bn are real numbers, with a1,,an nonzero. We also consider an analogous approximation problem in the space Sof temperate distribution on Rn.

Mathematical Subject Classification
Primary: 46.40
Milestones
Received: 16 February 1968
Published: 1 November 1969
Authors
Sav Roman Harasymiv