Uncertainty principles on weighted spheres, balls, and simplexes

Han Feng

doi:10.4153/CMB-2015-068-0

Uncertainty principles on weighted spheres, balls, and simplexes

Han Feng^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

This paper studies the uncertainty principle for spherical h-harmonic expansions on the unit sphere of Rd 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.

Original language	English
Pages (from-to)	62-72
Journal	Canadian Mathematical Bulletin
Volume	59
Issue number	1
DOIs	https://doi.org/10.4153/CMB-2015-068-0
Publication status	Published - 1 Mar 2016
Externally published	Yes

Research Keywords

Dunkl theory
Uncertainty principle

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title = "Uncertainty principles on weighted spheres, balls, and simplexes",

abstract = "This paper studies the uncertainty principle for spherical h-harmonic expansions on the unit sphere of Rd 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 = "Dunkl theory, Uncertainty principle",

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AU - Feng, Han

PY - 2016/3/1

Y1 - 2016/3/1

N2 - This paper studies the uncertainty principle for spherical h-harmonic expansions on the unit sphere of Rd 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.

AB - This paper studies the uncertainty principle for spherical h-harmonic expansions on the unit sphere of Rd 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.

KW - Dunkl theory

KW - Uncertainty principle

UR - https://www.scopus.com/pages/publications/84979561993

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84979561993&origin=recordpage

U2 - 10.4153/CMB-2015-068-0

DO - 10.4153/CMB-2015-068-0

M3 - RGC 21 - Publication in refereed journal

SN - 0008-4395

VL - 59

SP - 62

EP - 72

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 1

ER -

Uncertainty principles on weighted spheres, balls, and simplexes

Abstract

Research Keywords

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