Vol. 52, No. 2, 1974

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
An analogue of the Paley-Wiener theorem for certain function spaces on SL(2, C)

Andrew Bao-hwa Wang

Vol. 52 (1974), No. 2, 617–629
Abstract

The classical theorem of Paley-Wiener is concerned with characterizing Fourier transforms of C functions of compact support on the real line. It states that an entire holomorphic function F is the Fourier-Laplace transform of a C function on the real line R with support in |x|R it and only if for given integer m, there exists a constant Cm such that

|F(ξ + iη)| ≦ Cm (1 + |ξ + iη|)−m expR |η|, ξ,η ∈ R.
(1)

The purpose of this paper is to prove an analogue of this theorem for certain convolution subalgebras of C functions with compact support on the group SL(2,C), by using Fourier transform involving elementary spherical functions of general type δ.

Mathematical Subject Classification 2000
Primary: 43A75
Milestones
Received: 21 June 1973
Published: 1 June 1974
Authors
Andrew Bao-hwa Wang