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# Uncertainty Principles on Weighted Spheres, Balls and Simplexes

Published:2015-12-22
Printed: Mar 2016
• Han Feng,
Department of Mathematical and Statistical Sciences , University of Alberta, Edmonton, Alberta T6G 2G1
 Format: LaTeX MathJax PDF

## Abstract

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.
 Keywords: uncertainty principle, Dunkl theory
 MSC Classifications: 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

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