Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 55, Number 3 (2003), 451-466.
On Strichartz's uncertainty inequality for the Heisenberg group
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.
Tohoku Math. J. (2), Volume 55, Number 3 (2003), 451-466.
First available in Project Euclid: 11 April 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 43A80: Analysis on other specific Lie groups [See also 22Exx]
Secondary: 33C90: Applications
Smitha, Chettutty; Thangavelu, Sundaram. On Strichartz's uncertainty inequality for the Heisenberg group. Tohoku Math. J. (2) 55 (2003), no. 3, 451--466. doi:10.2748/tmj/1113247483. https://projecteuclid.org/euclid.tmj/1113247483