Uncertainty principles for Jacobi expansions
type: Item
instance of: scholarly article
title: Uncertainty principles for Jacobi expansions
zbMATH Open document ID: 1028.43008
DOI: 10.1016/S0022-247X(03)00507-9
author: Zhongkai Li
author: Limin Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-20T00:00:00Z
review text: Motivated by Heisenberg-Weyl-type inequalities on the torus and the sphere \(S^2\) by E. Breitenberger, F. J. Narcovich, and J. D. Ward, M. Rösler and the reviewer derived a sharp Heisenberg-Weyl-type uncertainty principle for general ultraspherical expansions of function on an interval some years ago by using an additional reflection operator in the spirit of Dunkl operators. For certain parameters, this uncertainty principle may be regarded as an uncertainty principle for radial functions on unit spheres. In the paper under review, this result is extended to expansions of functions in terms of Jacobi polynomials. In particular, again the optimality of the constants is achieved by considering suitable heat kernels. From a geometric point of view, the result may be seen for certain parameters as an uncertainty principle for radial functions on projective spaces.
reviewed by: Michael Voit
Mathematics Subject Classification ID: 43A75
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 2006349
zbMATH Keywords: uncertainty principle
zbMATH Keywords: Jacobi series
zbMATH Keywords: differential-difference operator
zbMATH Keywords: Heisenberg-Weyl inequality
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: heat kernels
zbMATH Keywords: radial functions
MaRDI profile type: Publication
cites work: Coherent States and the Number-Phase Uncertainty Relation
cites work: Uncertainty Principles and Signal Recovery
cites work: Differential-Difference Operators Associated to Reflection Groups
cites work: Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry
cites work: Conjugate Jacobi series and conjugate functions
cites work: HARDY SPACES FOR JACOBI EXPANSIONS I. THE BASIC THEORY
cites work: Q3374966
cites work: Classical Expansions and Their Relation to Conjugate Harmonic Functions
cites work: Nonstationary wavelets on the \(m\)-sphere for scattered data
cites work: An uncertainty principle for ultraspherical expansions
cites work: An uncertainty principle for Hankel transforms
cites work: Uncertainty principles in harmonic analysis
cites work: Q4061445
description: scientific article; zbMATH DE number 2006349