Tohoku Mathematical Journal
2005
September
SECOND SERIES VOL. 57, NO. 3

Tohoku Math. J.
57 (2005), 335-351

Title ON THEOREMS OF BEURLING AND HARDY FOR THE EUCLIDEAN MOTION GROUPS

Author Rudra P. Sarkar and Sundaram Thangavelu

(Received September 22, 2003, revised June 7, 2004)
Abstract. We establish an analogue of Beurling's uncertainty principle for the group Fourier transform on the Euclidean motion group. We also prove the most general version of Hardy's theorem on it which characterises functions on the motion group that are controlled by the heat kernel associated to the Laplacian of the Euclidean space.

2000 Mathematics Subject Classification. Primary 43A80; Secondary 22E.
Key words and phrases. Beurling's Theorem, Hardy's Theorem, Motion group.

To the top of this page

Back to the Contents