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Uncertainty Principles on Weighted Spheres, Balls, and Simplexes
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 1 / 01 March 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 62-72
- Print publication:
- 01 March 2016
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- Article
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This paper studies the uncertainty principle for spherical
$h$ -harmonic expansions on the unit sphere of 
${{\mathbb{R}}^{d}}$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the classical Heisenberg inequality. Our proof is motivated by a new decomposition of the Dunkl–Laplace–Beltrami operator on the weighted sphere.
