Tohoku Mathematical Journal

On Strichartz's uncertainty inequality for the Heisenberg group

Chettutty Smitha and Sundaram Thangavelu

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 55, Number 3 (2003), 451-466.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247483

Digital Object Identifier
doi:10.2748/tmj/1113247483

Mathematical Reviews number (MathSciNet)
MR1993865

Zentralblatt MATH identifier
1047.42010

Subjects
Primary: 43A80: Analysis on other specific Lie groups [See also 22Exx]
Secondary: 33C90: Applications

Keywords
Fourier transform Hermite and Laguerre functions spherical harmonics Heisenberg group representations

Citation

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


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References

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