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