Tohoku Mathematical Journal

On Strichartz's uncertainty inequality for the Heisenberg group

Chettutty Smitha and Sundaram Thangavelu

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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

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

First available in Project Euclid: 11 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Fourier transform Hermite and Laguerre functions spherical harmonics Heisenberg group representations


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.

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