Tohoku Mathematical Journal
2003

September
SECOND SERIES VOL. 55, NO. 3

Tohoku Math. J.
55 (2003), 451-466

Title ON STRICHARTZ'S UNCERTAINTY INEQUALITY FOR THE HEISENBERG GROUP

Author Chettutty Smitha and Sundaram Thangavelu

(Received August 20, 2001, revised April 10, 2003)
Abstract. The aim of this article is to obtain a lower bound for the variance of a normalised $L^2$ function on the Heisenberg group under the assumption that its Fourier transform is small along a sequence of well distributed rays in the Heisenberg fan. This is achieved by proving an uncertainty inequality for Laguerre series which is analogous to the one obtained by Strichartz for spherical harmonic expansions. Applications to Hermite and special Hermite expansions are also given.

2000 Mathematics Subject Classification. Primary 42B10; Secondary 43A85.

Key words and phrases. ourier transform, Hermite and Laguerre functions, spherical harmonics, Heisenberg group, representations.

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